I drove down to the launch point below the dam last weekend and the signs say no wading. You can launch a boat though. I wouldn't wade at the dam now with the way they do the sudden releases. Good way to die.
The water they let out is for electric generation, and seems to start about mid-day or so when the heat is on and the AC units turn on high. If there's a phone number I've never found it, the COE is closed-mouthed about release schedules. Don't know why but if you can get anything out of them please let all of us know.
The river gauge next to Dick's Canoes gives you a lot of pertinent information about flow rates and timing. Go here: http://water.weather.gov/ahps2/hydrograph.php?wfo=FWD&gage=AQLT2
With the current release pattern you could start a canoe at the dam at daylight and fish all the way down to Dicks before the river started coming up, as long as you keep a fairly steady pace.
When it's flowing it's fast. You could fish from a canoe but it will be difficult at best and possibly dangerous if you get too focused on the fishing part. Not sure how much you can catch zipping along like that but it would be a nice canoe trip anyway. About 6 hours from the dam to Dicks with a good flow rate.
There are other access points besides the dam. TPWD has leased three areas that you can access, to find out about them go here: http://tpwd.texas.gov/fishboat/fish/recreational/rivers/lease_access/
The further south you go the longer you'll have to wade before the river comes up. At Dick's the river isn't getting too high to wade until late in the afternoon and you can start wading at daylight.
Go on down to the other access points and you'll have a different schedule, maybe have to start late in the morning and can wade until dark, not sure but it's likely to be like that down there.
Best flys are woolyboogers, hellgramite imitations, and crawdad imitiations. Terrestrials can be pretty decent early and late in the day. Larger flys catch larger bass but fewer of them so it's a trade-off.
There are carp, usually in the deeper holes where you can't see them, and they are awfully hard to get to take a fly when you can see them. Then only way I've caught them is to spot a mud trail in the water, assume it's a carp actively rooting up the bottom, and to case upstream and let the streamer sink down to where the carp is feeding. Once in a blue moon that works. Mostly though you just won't see them. At least not in the area I fish.