A blend of the nouns slang and linguist, the noun slanguist designates:
– (original sense): a person who frequently uses or coins slang words and phrases;
– (in later use, also): a person who studies the use and historical development of slang.

The earliest occurrences of the noun slanguist that I have found are as follows, in chronological order:

1-: From Religious Poetry of ’71, by ‘A. B. Lasphemer, ᴀ. ᴍ.’, published in the Nebraska Advertiser (Brownville, Nebraska, USA) of Thursday 17^th August 1871 [Vol. 15, No. 44, page 1, column 3]—reprinted from Frank Leslie’s Illustrated Newspaper (New York City, New York, USA):

Mr. Editor:—[…] You should not allow your journal to be behind other publications in disseminating the beautiful morality of the slums and bagnios as it comes to us in its rugged grandeur through the writings of our great American sangwangists.
Feeling this, and having in my possession the writing of one of our profoundest slanguists, I venture to send you some of his recent poems.

2-: From “Befoa the Waugh”, published in The Osceola Times (Osceola, Arkansas, USA) of Saturday 26^th July 1873 [Vol. 4, No. 26, page 2, column 1]—John McClure (1834-1915), nicknamed Poker Jack, was a politician and judge in Arkansas:

There are a great many popular slang phrases in circulation of a recent date, which display the greatest perspicacity in their authors. […] The persons who first started these expressions into general circulation, possessed genius, but not of a creative character. They could observe, but not originate like the noble genius who gave the world that charming phrase, “Keiser don’t you want to buy a little dorg,” or, as we sometimes hear it varied by young gentleman [sic] just from some boarding school: “My dear Keiser, doth wish to purchase, or invest in a canine?” Among this latter class of slanguists, Poker Jack, or chief justice McClure as he is sometimes called, seems to be ambitious of a place. His claims as a slanguist rests [sic] upon a phrase of three words: “Befoa the waugh,” which is supposed to be some peculiar way of saying, “before the war.”

3-: From The Flowing Bowl. A Drama in 3 Acts, published in The Globe Drama: Original Plays by George M. Baker (Boston: Lee and Shepard, Publishers – New York: Charles T. Dillingham – 1885), by the U.S. playwright George Melville Baker (1832-1890) [page 7]:

(Enter ᴄ. Jessie.)
Jessie. Ha, ha, ha! such a racket! Students forever! There are those four college fellows who came down here to help in the dining-room, lounging on the rocks, while poor old Pete is frantically waving a napkin from the window of the pantry in which they have locked him. There’s music in the air, mammy, such a lark! (Sits ʀ.)
Mrs. M. Jessie Morris, haven’t I forbidden you to use slang?
Jessie. ’Spec’ you have, mammy; but it’s the proper caper in polite language, and so stunning! Besides, my Charlie is a slanguist; and you’ve often told me, with tears in your eyes, to pattern my conduct after his.
Mrs. M. “Stunning!” “Slanguist!” Jessie, you’ll drive me wild.

4-: From The Daily Morning Astorian (Astoria, Oregon, USA) of Thursday 28^th May 1885 [Vol. 23, No. 127, page 2, column 1]:

Mr. George Augustus Sala ¹, an eminent English journalist, wants to form an association for the protection of the English language. He thinks the slang that has crept, and is creeping into the language, is spoiling it. He thinks the phrases coined on the street are a disgrace to the good old Anglo-Saxon tongue.
Well, there is a good deal to be said on Mr. Sala’s side of the question. But there is considerable to say on the other side. Slang never gets into the dictionary. It rarely gets into any standard literary work. Then, too, slang is decidedly expressive. It undoubtedly voices the sentiment of the day better than any of the old phrases. It was necessary to coin something to meet the want. If the linguists didn’t coin what was needed it was only right that the slanguists should do something.
The slanguists are not very choice in their selections and inventions, it is true, but they did their best. If the linguists would tone down and improve the slang in existence, possibly some capital words could be produced as a permanent addition to the language. Let Mr. Sala form a combination of the linguist and slanguists and get out a revised edition of popular phrases.

¹ This refers to the British author and journalist George Augustus Sala (1828-1895).

The earliest occurrence that I have found of the noun slanguist used in the sense of a person who studies the use and historical development of slang is from The American Legion Monthly (Indianapolis, Indiana, USA) of December 1926 [Vol. 1, No. 6, page 79, column 1]:

THE war produced not alone a deluge of songs and poetry—it produced also a choice collection of new slang words and phrases. Comrade J. C. Ruppenthal, a judge advocate during the war and now district judge at Russell, Kansas, is interested in getting a collection of these words and phrases with their definitions. He says in his letter to The Company Clerk: “As a member of the American Dialect Society, I would ask whether some of your readers will not prepare a glossary of army and navy slang for your columns? This society for many years has collected dialect, provincialisms, slang, etc., from the entire country for preservation and to contribute to the history of the English language in its American variation. I have noted hundreds of terms myself but my fourteen months in the Army as judge advocate did not give me sufficient experience with army slang to prepare a vocabulary list. Then, too, I did not go overseas. Some of these words may persist in the language in some form. Some will no doubt be forgotten in a few years and will be meaningless except as preserved by students of the language of today.”
Here is a good opportunity for the slanguists to produce. Send your contributions to this collection to The Company Clerk in care of The American Legion Monthly, Indianapolis, Indiana. A blanket invitation is extended to everyone of every branch of service—doughboys, gobs, Marines, nurses, fliers, pill-rollers and all. We’re playing safe, as now and then The Company Clerk gets a bawling out for presumably slighting some particular branch but that is due largely to former members of that branch failing to produce.

A blend of the noun slang and of the adjective linguistic, the adjective slanguistic primarily refers to the frequent use or coinage of slang words and phrases—the earliest occurrences of slanguistic that I have found are as follows, in chronological order:

1-: From Local Police Court, published in the Bundarra & Tingha Advocate (Bundarra, New South Wales, Australia) of Saturday 19^th May 1906 [Vol. 6, No. 282, page 2, column 5]:

A gentleman with a Turkish name contributed to Cocky Carruthers’ ² funds the sums of 30/ and 6/ costs for slanguistic displays, the alternative being 7 days’ in King Edward’s board and lodging establishment on the hill. Option not accepted.

² This probably refers to Joseph Carruthers (1856-1932), Premier of New South Wales from 1904 to 1907.

2-: From a review of Maggie Pepper, by the British-born U.S. playwright and actor Charles Klein (1867-1915)—review by ‘J. R. G.’, published in The Pittsburgh Post (Pittsburgh, Pennsylvania, USA) of Tuesday 21^st January 1913 [71^st Year, No. 134, page 8, column 3]:

He [i.e., Charles Klein] has given the shop girl an opporunity [sic] to speak for herself from her own ground. It would be unlike Charles Klein to be without some purposeful axe of modern conditions to grind.
In drawing “Maggie Pepper,” the playwright has not forgotten his star’s preceding success in “The Chorus Lady,” she of the “slanguistic” dexterity. He has not failed to take advantage of so excellent an opportunity to provide Rose Stahl with the colloquialisms of the department store. Many of the laughs which waved over last night’s well filled house were won by Rose Stahl’s own manner of saying Charles Klein’s slang.

I have found an early occurrence of the noun slanguistics, designating the scientific study of slang, in Americanese and Australianese: A Disputation Inspired by Eggs, but Mainly on Language, by ‘Spartacus Smith’, published in The Sydney Mail (Sydney, New South Wales, Australia) of Wednesday 18^th November 1925 [New Series: Vol. 28, No. 712, page 2, column 4]:

Now that we are trying to get down to a general knowledge of each other’s languages to the end that a better opportunity will be given for the peace of the world, it is as well to have as good an understanding as possible. It is to be hoped that the students of slanguistics will modify their efforts. I am quite willing to accept language modulations, evolutionary construction of words, and even coinage […]. Dictionary compilers are known to have quite a number of new words held in reserve for future editions, pending the time—not very far off—when it will be forgotten that they were slang. The editor of the New Century dictionary has admitted to several, I believe. The fact that two English-speaking peoples find it necessary to ask explanations of the more cryptic expressions might be taken to indicate that some of us are in too much of a hurry to make a new language, and we will be in danger of having another Tower of Babel. Wars and other troubles are more easily hatched when people do not understand each other’s talk, and as English spreads all over the world, and is more likely to become the universal language than any other, I hope the lexicographers will put in the new words slowly and with caution.