Do Armor of Agathys and Fire Shield stack?


I have a party of a paladin, rogue, and warlock. The warlock player thinks having only 2 spells per short rest is making him really weak, so he is trying to find the best possible ways to be more useful.

So he is wondering if armor of Agathys and fire shield stack. I am wondering if he’s just power-gaming, or if this really does work and is the kind of thing a warlock is supposed to do.