You should be able to bring back some deleted files from flash memory, since most filesystems just mark them as deleted. The catch is that on magnetic media you can recover them unless those specific blocks have to be overwritten, while on flash/SSD you can only recover them if fewer than some critical number of blocks anywhere on the device have been written.
On average if N percent blocks are in use and therefore 1-N perfect blocks are free, once 1-N blocks have been rewritten anywhere on the device the blocks for your file will be gone. But since the controller isn't perfectly LRU and looking to coalesce used filesystem blocks to the larger NAND blocksize in practice you'd probably need a filesystem with fairly low write activity or catch your "oops I deleted a file I didn't mean to" pretty soon after the oops!
The nice thing is that once the blocks with critical data have been erased there is no way to bring it back. You don't need to worry about multiple overwrites to 'really' erase it per DOD standard any more than you need to write multiple times to RAM to erase it. Well, as far as I know. Maybe the NSA has figured out that a NAND cell retains 6% of charge after erase from a 0 but only 2% after erasure of a 1 and has some way to gather that info....if so an extra cycle or two of rewrites can't hurt if you want to erase data that if discovered could put you in jail for the rest of your life :)