Ah yes, flashcards that don't want to come out, how much do I love them...
I have a problem like this with my sky and in the DS Lite era I had the same problem with my DSTT. You know what I did? At the beginning I was pulling the card out with a tool or my own teeth. But then I figured out, why not make a handle? And so i did. Take a needle (I use an awl), make it hot under a fire like a candle or something, melt two small holes at the top corners of the card (you can open it, make the holes and put it back together if you are afraid of injuring the motherboard), pull strings through the holes and make knot them together to make a handle. I use bookbinding strings, because I'm a hobbyist handcrafted this things don't give me much problem.
Or you can just stick to using vice grips or something like that...