Fagela is a term used by some northeastern Jews meaning fag or faggot - i.e. a slur for a gay person. But is it an actual Yiddish word or a Yidlish[sup]1[/sup] backformation from faggot?
[sub]1. Pretty sure I just invented that.[/sub]
It’s faygeleh or feygeleh. It’s real Yiddish and it has nothing to do with faggot. It’s etymologically related to Yiddish foigel/German Vogel and literally means something like birdie, little bird.
Well, 715 hits on Google, so you didn’t invent it, but you did your bit to popularize it! 
ETA, and another 609 for Yiddlish. So your first job is going to be to standardize the spelling
Call someone who speaks spanish a pajaro (parrot/bird). Same idea.
ETA: “Yinglish” is the word OP’s looking for (Wiki entry), but I like yours too. Although it’s not Yinglish, it’s straight-up Yiddish.
My parents had a parakeet named Feygeleh, totally unaware of its other meaning until I enlightened them.
An earlier question that has some responses with the bird/homosexual connection.
Leo Rosten wrote “The Joys of Yiddish” in 1968. It is a dictionary of Yiddish words.
The definition of faygeleh is:
- little bird
- a girls name
- a dear little, sweet little,tiny, helpless, innocent child.
caution: use faygeleh for a little girl, not for a little boy,
because faygeleh also means: - Homosexual. Quite common (the word, not the libidinal arrangement)
in the American-Jewish vernacular. A synonym for the English “fairy” or “fag”.
Jews use faygeleh as a discreet way of describing a homosexual - especially
where they might be overheard.
So - yes, faygeleh has been in use as a term for male homosexual for a long time.
I recall one of my grandmas talking about how she could always spot a faygeleh because they were so obvious. She didn’t spot me, though. She might have spotted her son.
Others have corrected your spelling and basically replied but it really isn’t a slur as I’ve heard it used; just a way of saying gay person. What Yiddish I know I learned from working in the lodges during the glory days of the Poconos and I’m far from fluent but I believe there is another expression that could be used if one had the intentions of denigrating the individual.
The “eleh” is a diminutive or affectionate diminutive ending in Yiddish.
Cognate with “-lein” in High German, so “Vögelein”= “Feigele”
ISTM that this leaves the question still open. Even if faygeleh is a genuine Yiddish word, the original meaning has nothing to do with homosexuality, as you observe. So the question is whether the connotation of homosexuality is derived from the similarity to the English faggot or whether it arose independently.
Question then is whether this meaning exists in non-English speaking countries. Based on the cite from Rosten in post #7, it would seem that it does not. Which would suggest that it is indeed derived from faggot.
Rosten is pretty shwach oftentimes for scholarship.
Based on a cite from Leo Bloom in post #4, it would seem that it does.
[Quote=Leo Bloom]
Call someone who speaks spanish a pajaro (parrot/bird). Same idea.
[/quote]
I have no idea why you insist on making the English slang usage the root of this. It’s a false friend.
Aaah, now I see your point. Sorry.
Will give this some thought. It’s an interesting linguistics phenomenon.
No, Leo, you don’t have anything to apologize for. At least, not in this topic. 
You provided a counter-citation that Fotheringay-Phipps overlooked (the use of “bird” as codename for “homosexual” in a language completely unrelated to Yiddish.)
“Faggot” and “faygeleh” are false cognates; they’re etymologically unrelated in spite of the similarity of their sounds. (And I used “false friend” earlier when I meant “false cognate”. So mea culpa there.)
FWIW, “faggot” in English does have other uses, e.g., a bundle of sticks,/ for firewood or on a besom, and in some parts of England a meatball. In England it’s traditionally a pejorative word for a fussy/cantankerous/nosy old woman (possibly implying a witch?), which may be how it switched over to meaning a homosexual, though that seems to have happened in the USA, and relatively recently.
Plus, the sounds are not even that similar. The two words share an ‘f’ and a ‘g’, but that’s about it. Unless Americans are pronouncing “faggot” in a way that would surprise me greatly, the vowels are completely different.
You could always read a staff article by me How did “faggot” get to mean “male homosexual”?
The term faggot as a male homosexual goes back to 1914 in print in the US.
The thing about “faygele” is that it only has the meaning of “homosexual” in American Yiddish, and it first shows up after “faggot” and “fag”. So while faygele is an actual Yiddish word, the use of it as a slur could be derived from “fag”.