Learn English – Original Meaning of Blood is thicker than water, is it real

Can't help you with the origin of the phrase, but I suggest a more accurate rhetorical term for the phrase is MERISM.

Think of a merism as the counterpart to synecdoche, since both figures of speech concern parts and wholes. Synecdoche can be a

• part to whole substitution, as in "All hands on deck!" When the ship captain gives that order, he doesn't expect a bunch of severed hands to show up on deck. "Hands," therefore, is a part to the whole, the substitution of a body part for the whole body. In like fashion, when someone requests that you "count noses," they're asking you to take attendance, not to literally count proboscises! The nose--a part--is a substitute for the whole person.

• whole to a part substitution, as in "In my rearview mirror I could see the law as he approached my stopped car, and I could tell he was going to give me a speeding ticket." Here we have the whole, in this case "the law," substituting for the part; namely, a cop, or a state trooper, or an officer of the law.

Merism, on the other hand, expresses

• a totality--the whole--through contrasting parts, as in "The competition was open to all comers, both young and old and everyone in-between." Or, "Then the LORD God said, 'Behold, the man has become like one of Us, knowing good and evil' . . ." (Genesis 3:22a). Or, "She packed up all her possessions in record time: lock, stock, and barrel," meaning all, total, everything. (That merism may have had its genesis in the letters of Sir Walter Scott in, circa 1817.)

Merisms frequently figure in the writing of lawyers, and are a hallmark of legal style. The two parts of the legal merism "Last Will and Testament" at one time referred to two documents, enforced in two separate courts: the will disposed of a decedent's real property while the testament disposed of chattels. It became customary to combine the instruments in a single dispositive document, and the name has continued long after the doctrines that required its use became obsolete in common law.

A lawyer who writes a will typically includes a residuary clause that disposes of any property not covered by a prior section. The weight of tradition is such that the lawyer writing such a document will often phrase it something like this:

"I bequeath, convey, and devise the rest, residue, and remainder of my property, real or personal, and wheresoever it may be situated, to Sally Jones, of 456 Elm Street, Hanover, Massachusetts."

While the inclusion of merisms in a legal document might give the people who are paying the lawyer $400 an hour the feeling they're getting their money's worth, it does virtually nothing to make a given writing (or document) somehow "more legal"! Merisms also tend to obfuscate, rather than elucidate, a writing.

Some merisms were introduced during the period when Norman French words were being absorbed into English. In order to assure that a document was clear to both Normans and Saxons, it was desirable to use both the Saxon-root and French-root synonyms for important words, to avoid a pretext for someone to claim a misunderstanding.

Perhaps researching your "way, shape, or form" as a merism might go a long way toward finding out who was the first person to use the expression.

In conclusion, I did come across a modern use of your expression from Stefan Constantinescu's website IntoMobile, from Friday, November 27th, 2009.

"Walter Cronkite, the man, is in no way, shape, or form similar to Twitter, the medium"

Best wishes, and happy hunting!

Twiddling the Ngram arguments we find a "preprint" of @MarkBannister 's reference, in the May 16, 1914 issue of The Country Gentleman:

Remember the phrase how it's easy to get the boy out of the country but much more difficult to get the country out of the boy.

And there's a fair possibility that this is the first in-print use, as it's quoting Theodore Vail and uses "the phrase" rather than "the old phrase".