How can I attach Velcro to a fly screen?
What about velcroing through the screen, then sticking another piece on the back, basically making a velcro frame around the screen? This is hard to explain, here's a diagram:

AAAAAAAAAA
LLLLLLLLLL
SSSSSSSSSS
HHHHHHHHHH
AAAAAAAAAA
AAAAAAAAAA
LLLLLLLLLL

HHHHHHHHHH
AAAAAAAAAA
FFFFFFFFFF


The first 2 rows (AL) are one piece of velcro, loop side, with the adhesive away from the screen (leave the backing on this adhesive).

Next row is the screen (S)

Next 2 rows (HA) are another piece of velcro, hook side, again with adhesive away from the screen (backing removed from this piece).

Next 2 rows (AL) are another piece, loop side, adhesive against the previous piece so they stick back-to-back

Everything above here is on the screen (removable). Everything below is fixed to the wall.

The next 2 rows (HA) are the velcro stuck to the frame, and finally the F is the frame.