Yes, with that kind of coil you are going to get heat when you chain-vape. I'd also check to see if the coil is seated correctly, some smok coils are fabricated with some wire that needs to be dealt with that can cause flooding and poor wicking. If it continues with a new coil, you may want to take it in to a B&M and see if they can help you with it.
With that said, chain vaping can cause flooding of the coil, is it doing it consistently though, from the very first puff? If so, it's probably not chain vaping that's the cause of the flooding though it certainly would be the cause of the heat in your tank.
Best of luck,
Anna