Someone asked me this today and I really had no answer I know to be correct. A bit of Googling ascribed it to a similarity to a group of birds in ‘flight’, but that doesn’t sound right. One thing I found linked it to possibly being a calque (a linguistic borrowing or ‘loan-translation), via French wine stewards, from ‘volée’ of ‘volée d’escalier,’ literally ‘flight of stairs.’ That sounds more plausible, but I don’t speak French, so…???
Any nerds out there have the facts?
Wow, good question…
It’s very close to the bird thing.
A flight is a group of similar objects flying together.
Hence, the translation to wines being tasted in a group.
Perhaps by analogy to stairs because it’s a type of progression? Merriam Webster lists this as one definition of the word:
a : a continuous series of stairs from one landing or floor to another
b : a series (as of terraces or conveyors) resembling a flight of stairs
When not referring to flying, it’s used sometimes to mean a series or sequence of things. For example, you talk about a flight of stairs between floors or a flight of locks in a canal.
So a flight of wines would be a logical use of the word in the sense of referring to a sequence.
Well damn. What are the odds of three people typing the same response at the same time?
Thing is… I found all those but none of them seemed particularly conclusive. You’d think a term that widely used would have been thoroughly researched by now.
The stairs and birds answers are OK insofar as a ‘group’ reasoning, but most wine flights (at least these days) are generally not the same variety, although they certainly can be. Seems less than convincing that the linkage is that they are all ‘wines’. Just sayin’.
In vinous speak, it was originally a varying unit of wine and if your altitude is not high enough during or afterwards, you may have the option to book another, beware the purple tooth syndrome
Whose the third genius? I think it’s just you and me that saw the stairs connection.
Hmmm… seems to me that flight is a collective noun that is used to identify all sorts of groupings. Cheese flights, for example, might be grouped by texture, provenance, animal source of milk (goat, cow, etc.), and so on. Wines can be grouped into flights by grape variety, color, vintage, provenance, etc… (of course, today anything goes). In a tourney, golfers can be grouped into flights (often by similar handicap).
But the key thing is grouping, not sequencing.
This page says it comes from a flight of birds and says it only dates back to 1978 (which is hard to believe).
Dr. Vino agrees:
Low. That’s why, when it happens, it’s called a flight of answers. 
As indeed this was!
John - I was going to include Anton but if you want to include him out, that’s OK with me!
“Come flyyy, come fly with me…”
I don’t know about the use of the term for wine, but I never knew “flight of stairs” was calqued from French. I always just thought, like gratte-ciel, it was the other way around. You learn something new every day.
but most wine flights (at least these days) are generally not the same variety
Peter - that all depends on who you’re drinking with. Most of the time when I taste, they are indeed the same variety or varieties. But it is true that I’ve seen restaurants, etc., list what they call red flights, white flights, etc. I think the linking concept in those cases is simply wine, as there’s little, if any, logic to the progression.
But here’s a question - if you weren’t going to call it a flight, what would be a substitute word? Maybe somebody was just stumped one day and figured what the hell, I’ll just call it a flight, and thereby made history.
The Google ngram viewer is really fun. Wine flight as a term seems to date from the 60s.
I’m the Jerry/Larry Gergich of WB.
I guess I didn’t consider a “flight of birds” to be the same sense as a “flight of wine,” but maybe the bird meaning is more about the group than the action.