that said, I do not flyfish and pedal at the same time. The coordination to do that would be insane, especially given the need to operate the rudder. :-D
Simple answer, the pedals will not be much of a problem for your flyline, everything else will be however.
I usually sit side saddle when flyfishing, (Dangling legs over the side) and strip the line into the water, which takes some practice to strip to the side.
I would get a small anchor for the kayak, and use it to prevent the drift... May need two to use one for and one aft, with a Anchor Pulley system.