RGB LED flickering with PWM
Quick answer - no, you can't make this work without some hardware changes.

I certainly hope you're not connecting your PICs to 15 volts. They're only rated for 3.6 volts. 

Your MOSFET is not an IRL734. It might be an IRF734. In which case, I don't see how you're getting any output at all from the LEDs. What you want to do is connect the top of the LED chain to +12, and the bottom to a resistor. The other end of the resistor goes to the drain of the MOSFET, and the source goes to ground. If you know the operating current and voltage of the LEDs (and I hope you do), then the value of R is

R = (12 - (3 x Vf)) / i,  where i is in amps. 

Your driver would work (very briefly) if the PIC output were 12 volts, but it's not. I say briefly, because in very short order at least one of the LEDs would burn out. That's why you need a current limiting resistor.

Even with these changes, the circuit may not work well. The problem is that the PIC runs off 3.6 volts (max), while the threshold voltage for an IRF734 is two to four volts. And besides, the IRF734 is a 450 volt MOSFET, which is way overkill.

Given your obvious errors in circuit description (PIC voltage and MOSFET model), I suggest you go back to your source and provide a more complete (and accurate) description.

For what it's worth, 780 Hz is about 10 times faster than you need, but it ought to work just fine.