Not much. As I write this (the programs may grow a bit with updates), all six recommended utilities take up less than 25MB. I don't think you can buy a flash drive that small these days.
However, Tunz pointed out another issue on the forum. Flash drives generally are slow, and that makes the programs running off them slow, as well. A fast flash drive, like the Lexar JumpDrive Lightning or the Corsair Flash Voyager, may be worth the extra few dollars.
Read the original forum post.