Can you download adobe flash player on the iPod touch?

Adobe does not make a Flash Player that you can download to the iPod Touch, nor would Apple approve the app if they did. You can, however, use Skyfire as an alternative (assuming the flash is video), or, if you jailbreak your iPod Touch, you could try the "frash" application in Cydia (you'll have to add a repo to see it), though I haven't always had much success using it.