I lived there for 7 years, from 2008-2015, so hopefully some of this is still relevant. I lived on the Fort Worth side so this will be skewed some that way.
I preferred to fish rivers, mainly the Brazos below Possum Kingdom (Hwy 16; 32° 51.499'N, 98° 24.697'W) and Lake Whitney (31° 51.996'N, 97° 22.083'W). Both offer great bass and striper fishing. Below Possom gets stocked with trout. At Possum you can paddle both up an down stream from the launch with ease unless they are releasing. Below Whitney you go downstream and can come back up as long as they aren't generating (typical in the summer/early fall), but it's best to utilize Dick's shuttle service and fishing the 8ish mile stretch the entire day.
Urban Fishing in Fort Worth is an ok option on the Clear Fork Trinity and West Fork Trinity from Panther Island.
I did fish the east Fork Trinity River below Lavon (33° 1.371'N, 96° 28.517'W, launch can get muddied up) a couple times and kind of wish I fished it more often. At the launch it is dirtier water but down stream when you get past the powerline easement the river clears up. Lots of bass and it's where I caught a couple of bowfin.
I didn't spend too much time on the large reservoirs. I would fish from Sand Bass Point on Lake Grapevine for, well Sand Bass during the summer months. Trophy Club Park on the NW end of Grapevine gave easy access to Denton Creek for the Sand Bass run.
Ray Roberts was probably my favorite to fish. I preferred the north side of the lake launching from Johnson Branch SP or road easements or the east side on Buck Creek. If you don't have a GPS on your kayak, get
Martin's Map for Ray Roberts; extremely detailed and great to have.
I fished Lewisville quite a bit because I had a fishing buddy who lived on the lake, mostly for hybrids, white bass, sand bass and catfish. He was on a smaller cove, so the insane bot traffic was never really an issue; Willow Grove Park would be the closest public ramp where we fished.
Some smaller lakes to fish which are good are White Rock Lake. I never fished there, but I had a couple of friends who had figured it out and consistently caught bass. Would be a good spot to get your sea legs since they don't allow power boats. SE of Farmersville is a small lake (South Lake; 33° 8.166'N, 96° 20.802'W) which is great for kayakers, but does get quite a bit of pressure and during the summer months the shorelines do get thick with vegetation. Near Prosper was a small community lake (33° 14.509'N, 96° 45.602'W) which when I was there, was still an option to kayak fish. It used to kick out some decent bass, but it may get too much pressure these days. Over in Canton is Canton Lake (32° 32.217'N, 95° 51.004'W), and it is a fantastic little lake and worth the drive. Go on First Monday weekends and drop the misses off to shop and you go fishing. Over in Fort Worth, Marine Creek Reservoir is a small lake, but holds big bass.
The two National Grasslands Caddo and LBJ offer great little lakes for kayakers. I never made it to Caddo, but the consensus was Coffee Mill was the better of the two ponds up there. I did fish LBJ Grasslands quite a bit and spent most of my time at Clear and Rhodes lakes. Nothing of size, but good numbers lakes. There are about 9 ponds at LBJ Grassland that are big enough to kayak.
I hope some of this information is still relevant.