This is a strange, yet amusing question. Firstly, let me trot out the obligatory PC-isms: gay people are not a monolith, and they cannot lay claim to any particular style, hair or otherwise. Go to a modern EDM festival, say, and you will not be able to distinguish between the gay and straight boys by style and appearance alone.
In the 1950’s and 1960’s, the Flat-Top was considered the most ultra-masculine hairstyle a guy could have. A true Flat-Top we’re speaking of— not a mere Burr or Crew cut— in which the barber literally clippers a flat “table” on the top of your head, which he calibrates with a special big comb for perfect evenness. Butch wax— a thick gummy pomade— usually needed to make the hairs stand straight up. The Flat-Top was especially seen on football and basketball players, bodybuilders, law enforcement personnel, wrestlers and boxers, college fraternity boys and most memorably, the American astronauts and NASA personnel. It told the world you were a vigorous, sportive, outdoorsy jock, who didn’t have time to fiddle with his hair. The Flat-Top is not really a military style per-se, as most military men would either clipper almost everything off to form a Scunion, or they’d have it done in a High ’n’ Tight, which trims only the back and sides, leaving some longer combover hair on top.
When long hairstyles for men emerged in the mid-to-late 1960’s, they stood in stark contrast to the Flat-Top, and indeed, both hairstyles became a political statement: e.g. whether one supported the Vietnam War or not, whether one dabbled or not in illicit substances, whether one advocated Free Love or conventional marriage, whether you listened to Rock or to C&W. Men from the American South especially clung onto the Flat-Top years after it became outdated elsewhere in the USA.
But, since about 1990 or so, gay men have often appropriated styles that used to be considered only the province of straight men (as well they should). And vice-versa. Rigid gay/straight divisors are rapidly becoming old-hat and provincial. Most young men today simply dress and groom as they please, and their look need not necessarily “signify” anything. (Ditto with wearing earrings and having tattoos put on).
If you decided to get your hair cut in Flat-Top today, people wouldn’t likely think it “gay” at all. They’d probably think you were going for an ultra-masculine, aggressively sportive, and yes, decidedly oldschool or Midcentury kind of look. Or you were someone who often wore a helmet. Or maybe they’d think you were apeing the look of some Punk rock group. Or if you are Black, you are going for an oldschool 1990’s “rise”.
<<addendum:>> I do see that the modified flat-top is becoming a hipster variant. I like the look very much. It looks assertively masculine, maybe slightly martial? Some men can wear it better than others, ’tis true: helps if you have a nice head-shape, and ears that aren’t too big. Blond men especially can pull it off nicely.
If the hair on top is a good bit longer, it starts to look Punk Rock-like, like a Mohawk.
An oldschool variant of the Flat-Top is the so-called “Flat Top Boogie”, in which the sides and the back of the head are NOT razored, but rather left longer and combed back with a pomade. This little forelock seems to have been this singer’s own Rockabilly touch.