You can only downgrade to a firmware built for that Kindle model.
Currently the KT2 (Kindle Touch 2/New Kindle Basic) and KV cannot be jailbroken.
One MobileRead member has successfully jailbroken manually, with a serial cable.
https://www.mobileread.com/forums/showthread.php?t=247480
We must wait for JBPatch to be updated for the KT2. Hopefully someone will come up with new goodies.
First we need an easy jailbreak.