IC555 flyback driver troubleshooting
You should consider interfacing the 555 indirectly to the MOSFET for a couple of reasons: -


The gate capacitance of the MOSFET (circa 1nF) likely means that the waveform output from the 555 is being turned from a nice looking squarewave into a more triangular shape and this will cause the 555 some stress and be not ideal for driving a FET used in a flyback transformer circuit.
The output capacitance of the FET can couple significant energy from the transformer primary to the gate when switching and this may also be causing the 555 a lot of stress. Assuming you are running the circuit from 12V, the primary winding will likely be seeing 24Vp-p (as per a regular flyback design) and if you imaging this couple via (say) 100pF to the 555's output you might understand what I'm hinting at.


There may be other things wrong with your design but I would definitely consider using a high current logic driver to feed the gate. The gate driver should be able to deliver about an amp into the gate in order to charge and discharge the gate's capacitance up quickly.

With a poor driver you might also be getting an instability when the FET switches. When it turns off (gate attempts to go low), the output rises quickly and with the inter-lead capacitance this rising voltage can couple to the gate and cause it to momentarily switch off partially. Again it will warm up the FET and if it happens on the rising edge it will likely happen on the falling edge of the drain voltage.