The "beer" is significant. Among males of the species, "Having a beer" is a behavior used to demonstrate that one is "one of the guys". So, "needing a beer to put flames out" seems to be like doing a "man's thing" to wash away any feminine or effete appearance. ("flames" - meaning "flaming" or gay attributes)
I agree that the Obvious meaning may be that he was "shot down in flames" , or rejected, by the female - however, in keeping w/ OP's question, I submit that an alternate meaning is: He believes he is being rejected because SHE perceives him as gay.