I have hunted out of a "kayak" for the last 10 or 12 years here. I hunt two streams, the Savannah River and Brier Creek. The creek is actually a pretty big stream in many places, with plenty deep enough water to drown you in places, and the big Sav. River, well it can be downright treacherous in places.
I have devised my own system of jump shooting these streams. I have to wear full camo, preferably a dull grayish pattern like the old M.O. Breakup. I have to black my face, because I can't stand a face mask. They drive me nuts.
The half of the kayak paddle you see in the photos is tied with a rope or cord and is tied off to my belt. I am right-handed, so I keep my shotgun in my left hand, safety off, muzzle up and kind of scull with the short paddle in my right. When ducks flush I drop the paddle in the water, grab the gun with my right hand and shoot. As has been mentioned, shooting from a kayak, where you are basically sitting flat on the bottom, is hard at best. I used to keep the gun between my legs and paddle with both hands, but that doesn't work jump shooting. Too slow.
On smaller streams like Brier Creek there are ducks sitting along both sides, usually behind some cover like a downed treetop, or big tree trunk. For a right-handed shooter a left curve in creek is the most promising. You must remain
ABSOLUTELY motionless as you drift around the bend if you want to get the jump on them.
On the big rivers here the willows are always on the inside of the bends. The opposite bank will have a high bank and no willows. Willows are where the ducks are going to be. You need to cross over to position yourself right to ease around the curve next to the willows. Done right you can get within handshaking distance at times. Move any at all, and forget it.
My rig is stable as long as my butt is on the bottom. Raise up on one knee to relieve yourself, and all bets are off. I've never rolled it in all these years, but, I've come very close.
These are built by a guy down around Lake Okeechobee, FL. It is about 12 ft. long, very light weight hand laid fiberglass, and weighs about 28 lbs. It had a dark brownish green paint job when I got it, but it had a gel coat that was reflective, so I repainted it in flat colors I liked better.
I've killed a lot of ducks with this rig, but
I've missed a lot, too!!

SRH