I would think as long as its heated to above 150 you should be alright.
There's a lot to read in the food safety threads, one that sticks with me from K Kruger has always been this
(the first is from Kruger, the 2nd is equally relevant, unfortunately):
(((from the
Poor Richard Almanack)))
Here's the Kruger Safety Compilation:
https://tvwbb.com/showthread.php?39803-The-Kruger-Safety-Compilation-v0-1
I'll boil it down to this

(I spent a lot of time reading, and as with many subjects, I read a lot more than I understand):
Raw meat has spoilage bacteria that will compete with the pathogens whose byproduct is toxins that makes us sick or kills us. The spoilage bacteria may make chicken slimy and smell, but you can cook raw meat that's been mishandled, to a safe temperature, and even though its flavor may be off, it is safe to eat.
Meat that's been cooked doesn't have that spoilage bacteria to compete with the pathogens anymore, and the toxins the pathogens excrete are basically invisible and tasteless, but can be very dangerous. ((My dad's best friend's wife died from bad Chinese in 2005)).
As for safe time in the fridge???? I don't know. I try to cool/fridge/freeze as best I can, and if I see someone's twice boiled meat once, I probably won't eat anything they've made that I didn't see. A week is probably safe, but my personal comfort limit on uncured meats (cured or meats packaged in cryovac are different) would be limited to maybe 5 days. Boiling again probably won't remove the toxins. I'm no expert, that's just my personal understanding, most of my sources, and reasoning. HTH.