Origin of "tail over teakettle"?
The earliest instance of "tail over teakettle" in the Ngram results that Josh61 reports is from Everybody's Magazine (1927) [combined snippets]:
Henry sees her, gives a flip of his tail and capers to her, thinkin', maybe, he's found another little playmate. Gravy sees him comin' and stands watchin' the cat with her ears pricked forward. Henry puts out a friendly paw. Gravy whirls, lashes out with her hind feet and lands on Henry's ribs—biff—biff—and knocks him tail over teakettle.
And the earliest instance of "ass over teakettle" in those results is from Richard Johns, Pagany, volume 3 (1932) [combined snippets]:
Well, your lucky. If I was him I would of fired you ass over teakettle out of the place on the spot for carelessness.
But a more general search for matches to "over tea kettle" and "over teakettle": turns up an earlier phrase than either of these: "heels over tea-kettle." From Alfred Damon Runyon, "Fat Fallon," in Lippincott's Magazine (October 1907):
'Luff, you lubber, luff!' bawls Fat, dancing about on the edge of the bow until I expected him to go heels over tea-kettle into the lake.
Two years later the phrase "head over teakettle" appears. From Maximilian Foster, "The Red Block," in Everybody's Magazine (August 1909):
"But the furnace boss he don't pay any particular attention. 'Goramighty, man!' says he; 'ye c'd fire every hobo in the hull dummed outfit, head over teakettle,' he says, 'was ye only to git me coke enough to to keep runnin'! Gosh!' says he; 'if they ain't coke in this yere yard in twelve hour by the clock, that there stack o' mine'll be froze up harder an' tighter'n old gran'par's pocket-book. ...'"
The same search also turns up an instance of "tail over tea-kettle" probably from the late 1910s. From The Aeroplane, volume 9 (1915[?]) [combined snippets]:
What is the special—and singularly non-apparent—reason for that economy and regularity of speed? and how does the Green motor manage to give its full power, no matter whether it be standing on its tail or driving on its nose, or even turning tail over tea-kettle during a looping stunt?
Since the Google Books result here was shown in snippet view only, I can't confirm the date, but the search result page specifies volume 9, 1915; elsewhere I found copies of The Aeroplane volume 6 dated 1914 and volume 20 dated 1921, suggesting that if the volume number of the Google Books item is correct, the actual year of publication of the cited quotation would be 1917.
The earliest confirmed Google Books match acknowledging the cruder wording of the phrase is in a letter to Bonamy Dobrée dated September 29, 1927, letter from T.S. Eliot, published in The Letters of T.S. Eliot: 1926–1927 (2012), containing the poetical line "In fact Tea-Kettle-Arse-Over." The editor of this volume dedicates the following footnote to the phrase:
1—'Arse over tea-kettle': US slang: an equivalent of 'arse over tip', or 'head over heels'.
I suspect that the word arse was rather less common in the United States in the 1920s than the editor imagined. But more significant than Eliot's anglicization of ass in his letter is his invoking the phrase "ass over teakettle" at all. If it is indeed a U.S. phrase, Eliot may have encountered it prior to his emigration to the UK in 1914. It certainly makes sense that coarse versions of colloquial phrases might find their way into print somewhat more slowly than euphemistic or bowdlerized versions of the same. The fact that the two earliest matches for "X over teakettle" give X as heels in one instance and head in the other suggest that the metaphorical identity of the teakettle itself were not especially well understood by the writers offering the euphemisms.
J.E. Lighter, The Random House Historical Dictionary of American Slang (1994) notes such alternative "ass over X" formulations—all with the meaning "head over heels"—as "ass over tit" (from 1938), "ass over appetite" (from 1942), and "but over teacups" (from 1954). Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995), on the other hand, considers the original wording in the United States to have been "ass over tincups" and reports the phrase as "a variant of the early-20th-century British arse over tip."
The only slang meaning of teakettle by itself that I've found in U.S. slang dictionaries is from Harold Wentorth & Stuart Flexner, Dictionary of American Slang, first edition (1960):
teakettle n. An old locomotive. 1952: [example omitted] Railroad use.
But this doesn't seem particularly relevant to the "tail over teakettle" idiom.
In Maine, a man's equipment is called his teapot or tea kettle. So, if he goes ass over tea kettle, well you get the picture.