Will using a normal 8 GB flash drive in an Xbox 360 Slim work?

Yes, that flash drive will work. I used to use that one for my old Xbox for more memory space. You can save anything on here except for games you install from disc, that doesn't mean arcade games, only full games. Extra map packs and other DLC will work, but when I used to use it I remember it used to make me lag on games. Because it has to read off of the USB and it is slower than reading of the Hard Drive or the built in 4GB in the 360. I notice you only asked if they make 20-40GB HDDs. The answer is yes, but they also have a 250GB for about the same as a 40GB HDD for the Xbox 360 Slim. It's not an official Xbox HDD, but it functions the same. If I were you I would buy the 250HDD for half the price of the MS one. I put the link of the hard drive in the source link.