No, it's not "Tail Rot", which is an active infection that spreads up the tail towards the body, killing all of the tissue along it's way (you'd know Tail Rot, trust me, the dead tissue turns black, shrivels, and falls off). The kink in the tail is most likely due to a Calcium Deficiency, if it got caught in a door or something similar and their is a Calcium Deficiency, it will not heal completely.
I highly suggest buying a brand new T5-strength UVB tube, best place is Amazon.com, cheapest place anyway. A 22" Reptisun 10.0 T5HO UVB tube and a 24" T5-rated fixture for it will cost you under $50 shipped, and they are double the strength of the much weaker T8 strength tubes. Plus, the T8 tubes must be replaced once every 6 months, while the T5 tubes only need replaced once every year. They also don't have to be as close to him as the T8 tubes (6") but rather only 11". So this should help him recover from any start of MBD and keep him healthy from this point on. The kink in the tail will always be there, but it won't cause any harm or become infected.