IGBT gate driver burned, why?
There are plenty of reasons that can cause IGBTs blowing. 

  Here are just some suspect points regarding IGBTs.
A) Your 2 IGBT connection look suspicious. PS-Collectro-Emitter-Emitter-Collector-Load?
B) Driver output resistors according DS - top one 3 times bigger than bottom one. In your circuit they are both 20R.
C) Wires that goes to Gate should be as short as possible (avoiding parasitic inductance).
D) Parameters of Driver and IGBTs must match each other. Double check things like Driver output voltage and current, IGBT gate charge, threshold voltage, switching frequency. 
Most time these kind of circuits require very detail design and step by step debugging with oscilloscope. For your and others better understanding SCH design must be done properly not just draft on paper with pen. Your time learning any free available CAD tolls will definitely worth it considering possible losses.