The question is in the title.

Maybe, depends on the way the frame is constructed.
there are clamp in between the chainstay ideally on plate types,
clamp across the rear left side of the rear triangle,
and those which clamp in under the left axle nut.

You can buy one for any wheel size to clamp on to a variety of places. Google?

Flip the bike upside down.

you can just buy a normal one and have an lbs cut it down. we do it all the time for kid's bikes.

Already tried that, but the kickstand of another of my bikes(that I'm not using any more) did not fit my BMX.
Are there any kickstands that are designed for BMX bikes?

If you want to lose all street cred available to you, then yes, there are. Just go to your LBS and tell them what you're looking for.

I disagree. Aftermarket heat-treated 4140 kickstands open up all new possibilities as far as grinds go.