The reason this is confusing is because there are two separate interpretations of the same line. Although both have been covered separately here, no answer covers why there are two interpretations in the first place.
First, the straightforward interpretation: Either his heart is "on fire," or (as per medica) he's been shot down (romantically) and is on fire like a burning plane.
Either way, he's going to douse the flames with a beer (i.e. forget about his heartbreak by drinking).
The alternate interpretation comes out of the fact that many famous movies, particularly those focused on a close male friendship, have a veiled gay subtext. It rarely seems to hurt any given movie among straight audiences, and can boost it among gay audiences (depending on how it is handled). Sometimes this is relatively blatant and played for laughs ("Some Like it Hot", "Without a Paddle"). Other times, it's more hidden. In the Golden Age of Hollywood, gay screenwriters like Gore Vidal often deliberately hid homoerotic imagery and double entendres in mainstream films ("Ben-Hur") as a subversive act of silent protest against prevailing homophobic norms.
The macho buddy movie Top Gun, starring the often-rumored-to-be-gay Tom Cruise, has long been identified as having a hidden gay subtext, even before Quentin Tarantino popularized the theory in the film Sleep with Me. There are any number of places to find the movie reinterpreted in this way, from the compilation you referenced to entire websites. While there's a strong case to be made for the movie as a whole, many of the individual interpretations are a bit of a stretch. In this case, the compiler is implying that Cruise's character is trying to drink away the fact that he's a "flaming" homosexual. While that could be a joke from some clever screenwriter, it doesn't make much sense in context.