The first thing I would do is create a sketch that simply cycled through red, green, and yellow values, just like what the Arduino would receive if the red slider was moved through its full range, followed by the green slider, followed by the red slider.
If the LEDs still flicker, the problem is not with Processing or Firmata. If the LEDs don't flicker, then it is.
If they do, I'd dump firmata and write my own protocol. You are sending three bytes to the Arduino, although Processing converts the values to strings, and the Arduino converts them back. That takes a not-insignificant bit of time. Send a start of packet marker, three bytes, and an end of packet marker ("<", r, g, b ">", for example).
On the Arduino, look for the start of packet marker. Then read the next 4 bytes. If the 4th byte is the end of packet marker, use the 3 bytes before it. If not, a byte got fropped, so discard the packet.