Why are my MOSFETs burnt?
There are three possible causes I can think of that would cause the FETs to be damaged:

1) Over dissipation.  You say the LEDs are 15W - how much current is that?  Do the FETs get hot?What voltage are they being driven from?  How fast is the multiplexing from the TLC5940? If the gate drive is not enough to ensure saturation they could get excessively hot and be damaged.

2) Over voltage.  You have no snubbers (an R and C) on the outputs to dissipate voltage spikes if there is inductance in the wiring, you could get these spikes at turn-off of the FETs.

3) SOA violation: Is there excess capacitance on the output lines that could cause excessive currents at turn-on of the FETs.

To start with I would look in detail at the turn on and turn off of the output stages.  Ensure there is enough gate drive, that the drain voltage goes down to a very low voltage when the FET is on.  Look for spikes at the drain when the FET turns off.

Looking at the FET current is not so easy - a low value resistor in the source of one of the FETs would be one way or a current probe.