I'm very, very, very late to the party on this one and you've probably already changed your impression of this on your own but I'll just put this one out here since it's likely to be found on search engines

James from Pokémon is not 'gay', or at least, is never outrightly shown to be 'gay' in the series.

There's a name that people use for his behaviour, which is sometimes associated with being gay, and that is called "Flamboyant."

James has a "flamboyant" personality, or; his personality is full of flamboyance (look it up on wikipedia)

As far as one can see in the show, he is heterosexual.

Heterosexual is the official name used for a woman who likes men, or a man that likes women. 'Straight' is slang for heterosexual

Homosexual is the official name used for women who like women, and men who like men. 'Gay' is slang for homosexual. Or just; "Homo"

Bisexual is the official name for a man or a woman, who likes both men and women.

There's other more complicated names for sexual preference in general as you get older but those are basically all you need to know until it's relevant to an essay or someone you know.

James falls for many women in the show, kind of like Brock, but never usually as head-over-heels as Brock is to every woman he meets, thus, as far as we know it, he's heterosexual.