Don't make flash cards or mnemonics. Just PLAY the darn things. Go through the circle of fourths in order. Start on C, then figure in your head what the fourth of that is, and you know that that has one flat. Play that. Figure out the fourth. Play it. Do this as many times as it takes until you can easily identify key or signature, and play it. Then, play them in random orders just to make sure, until you can instantly spit it out. It is NOT that hard, except in the beginning, but it goes much faster than you'd think.
After 7 years of playing and reading music on a regular basis, I still could never identify a key by number of flats or name until my teacher forced me to do this.
If you've done that, congratulations, you're miles ahead of the vast majority of all musicians, and well on your way to becoming someone who knows what they're doing.
And of course once you've done that with major keys, move on to minors, and mix in majors, too, to keep in practice.
+1 When I went through theory, there was the whole memorizing-the-keys thing. It ended up being useless busy work. What was useful was pulling apart intervals, chords and scales and putting them back together to see how they worked.