Will any net curtain keep out flea beetle?

I would try using the finer net curtains and it should help. Weak points would be at the base so if you lay a length of board on every side and weight down the board, that should minimize entry.

It's possible that some flea beetles might already be in the patch so if you have any insecticidal soap to spray it on the soil and under leaves first and then cover with the curtains. That should give you a better chance.

I personally would make whatever sort of cage I could so the netting won't sit right on the veg where the pests can still attack it - even through netting. Even a few inches of space will make a huge difference.