Not sure what fop2 version you have installed. Flash is just a fallback mechanism, since version 2.25 FOP2 uses websockets.... since version 2.27 it supports secure web sockets.. So for better compatiblity with modern browsers you must be running at least version 2.27 and it would be best you are running the latest one 2.31.09. If running 2.27 or above, and you use https to connect, you must configure the ssl_* parameters in fop2.cfg correctly (matching your web server ssl certificates config).
Best regards,