I see three flags:
Left center appears to have 3 vertically oriented stripes, with a dark stripe closest to the staff; based on @Justcal 's comment, this is probably France.
Center right which is more properly a pennant or ensign than a flag and dark with a yellow rosette. Quite possibly the Japanese Imperial Banner. (Hat tip to @ezekiel and @justcal )
Lower right and has horizontal red and white stripes below a starred field. The third is probably USA (@mark points out that it is more properly "American-ish", but I don't think the cartoonist intended accuracy)
Although you didn't ask, I see several different uniforms depicted, and that might help to confirm the flags.
Left - red caps, blue jackets, red pants. @ AmiralPatate points out that "Uniform on the left looks to be the French uniform that was notoriously bright blue and red until 1914, when it was decided it wasn't a very good color scheme for modern warfare after all."
Center left - Dark uniforms with vertical seamstripe and characteristic pickelhaube helmet. No flag present, but I would guess German
Foreground right - white uniforms with distinctive furred caps. No flag present.
Foreground further right - red jackets and a helmet which suggests Great Britain
Foreground right - Dark jacket, dark trousers, gold epaulets , gold trouser stripe - looks very USA.
The brown, triangular banner with yellow ?flower? is being carried by men in a canoe, and they are wearing what look to be Hawaiian feather helmets and cloaks, while carrying wooden staffs, as seen in this Rembrandt Peale picture.
Thus, -- given that Japanese were part of the Yellow Peril -- it's some sort of Hawaiian war banner.