I don't think that any general purpose software would be able to take Kindle snapshots.
However Kindle has Rescue Mode which most likely can completely reflash main Kindle partition block by block.
So to get backup/restore functionality on Kindle you'll need figure out how to do 3 things:
1) Find where main partition is stored on the flash chip and dump it to user accessible partition
2) Figure out how to convert it to binary update format
3) Figure out to to create updates that would install from rescue mode. No one was able to do it so far.
I know a little bit of linux but not enough to do all the things mentioned with reasonable effort.