(edited as requested)
A common talking point I've heard regarding the most common of homophobic slurs is that the word which also means a bundle of sticks for starting a fire/ kindling, became associated with homosexuals because of their being burned at the stake contemporaneously with witches. Is this true? Were gay people burnt at the stake during say, The Inquisition or the Salem Witch Trials? If that's not the case how the word end up becoming a slur?
OP, while you might get answers in this sub, this is more of an etymology question. You might try x-posting to /r/etymology (although note that it is a recreational/hobby sub, not academic) or take a look for a good dictionary (every dictionary includes at least some etymological info) or a specialist etymology dictionary.
As it happens, though, this question has come up a few times here, so you can take a scan through some earlier responses
Were homosexuals burned at the stake in premodern Europe? featuring /u/Adeptpotato - tl;dr no they weren't
Where does the term "faggot" come from historically? featuring /u/theshowisnottheshow - tl;dr possibly it referred to old women who gathered kindling
Homophobic slurs in turn-of-the-century/WWI Britain? featuring /u/heisengirl and /u/NMW - tl;dr maybe it's more complicated than that