I know that level one cloaking last 5 seconds, level 2 cloaking lasts 10 seconds, level 3 cloaking last 15 seconds. But how long does it take to recharge?
According to this wiki page (and as Skeptical Chymist mentioned), a cloaking device requires 4 lapses of ion damage recovery to recharge.
This other wiki page says that "for each ion damage a weapon causes, the cooldown increases by five seconds"; a cloaking device would therefore take 20 seconds to recharge.
It requires 4 lapses of ion damage recovery - basically, at the cloak icon, after cloaking, it will display a little countdown thing. This starts at 4 and counts down to 0. Note that it isn't really disabled by ion damage after you use it, or it doesn't have to - it just represents that the use of the machine has been temporarily disabled.