I had never heard of this movie and did a little search on line to check if my understanding was likely. Indeed it is in keeping with what I could read online. And some critics say the film is homophobic.

Être de la jaquette is a colloquial (slightly derogatory) term to qualify a homosexual and not much used nowadays.

The original phrase is être de la jaquette or être de la jaquette flottante but some people say de la jaquette volante (I have found quotes with jaquette volante online but I do not want to link to them, those sites are too offensive). You can find the etymology and meaning of être de la jaquette on the wiktionary.

I think the translation you found ("Do you swing the other way?"), although it conveys the meaning, is too soft. I would translate "Do you swing the other way?" by: es-tu de l’autre bord?¹

^{1Être de l’autre bord on the wiktionary, entry 2.}