You can do it from the 16 bridge when the gates are closed. They are closed now. You'll need to walk your kayak to the deeper still water by the bridge and launch.
Here's what the entrance looks like in normal flow
When the gates are open you can drive up to the dam and there's a small stream that goes into the brazos there that you can put into. I've seen kayaks put in there, but I considered it having a death wish when the water was high.
Here's what the entrance looks like by the dam
These guys did it and lived
But are you sure you want to kayak in this?