Drive multiple LEDs at different voltages from a low current I/O
First: Two LEDs if operated with identical current, will in practice have different intensities, due to manufacturing tolerances even between LEDs from a single batch. This is not easily perceptible when the LEDs are at high intensity, say the 10 to 20 mA range for your 20 mA LEDs, but the differences become very visible as the LEDs are dimmed. 

Now, there are a few things that need improvement in the schematic. For instance:


The potentiometer at the 6.5 Volt rail: 
Not needed.
LEDs are current-driven devices. So long as you supply the right polarity of supply and limit the current through each LED chip with an appropriately calculated resistor in series as you have shown, the supply voltage should be the 6.5 Volt line directly.
Anything above about 4.5 Volts will work - 3.2 Volts for the green and blue LED's maximum, plus some headroom for the transistor's VCEsat and for regulation by the resistor.
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Why not use the potentiometer anyway?
It will need to dissipate power corresponding to the entire current drawn by all 6 LED junctions, so up to 120 mA, times whatever voltage is being dropped across the active part of the potentiometer. That'll require a high power rating pot. Also there will be heat generated on that one part, rather than distributed across several individual current limiting resistors that the schematic already has. 
Why the 6.5 Volt supply? A 5 Volts supply, if available, would reduce wasted power and generated heat at the current limiting resistors. 


I am sure others will chime in with other suggestions, but those are a start.