Since knowing *perfect* basic strategy will still have you at a disadvantage in this game, I would know it perfectly without question before going into a casino.
It should be the absolute minimum level of knowledge/skill you walk into a casino with.
I also did the flashcard thing, and it helped a lot. I would write the entire chart down on a sheet of paper, then I'd do it in random order, then I'd draw out the chart from memory too.
The thing that helped me at first was learning the moves in "real words" as opposed to memorizing coloured squares on a chart. Like:
A,2 double 5-6, o/w hit
A,3 double 5-6, o/w hit
6,6 split 2-6, o/w hit
7,7 split 2-7, o/w hit
... etc.
I'd just say it to myself over and over. I have it typed out on a small piece of paper and kept it with me all the time. In traffic or whatever, I'd pull it out and go over it.
Just keep going over and over it until it's second nature. You shouldn't even have to think about what the proper move is, you should just react to the cards and instantly know what to do. Then you can spend more brain cycles on counting, betting, and trying to get the blonde at third base's phone number.