Ok, in general, with r Red, b Blue and g Green chameleons:
It is possible to get all Chameleons of the same colour, according to the rules, if and only if:
r==b (mod 3) OR (all Chameleons green at the end)
r==g (mod 3) OR (all Chameleons blue at the end)
b==g (mod 3) (all Chameleons red at the end)

Of course, if they are all equal, then you can choose which colour chameleon to have at the end.

You can actually figure out the minimum number of moves, based on which two are equal (mod 3).
i.e. 4 red, 1 blue, 3 green (4==1(mod 3))
4,1,3 ->
3,3,2 ->
2,2,4 ->
1,1,6 ->
0,0,8 = 4 moves
I *think* it is simply whichever of the two is the largest.
Think about 28 red, 1 blue, 2 green (28==1(mod 3))
28,1,2 -> (6 moves, RG->BB twice, RB->GG 4 times)
22,1,8, which is basically the same, but 28 has decreased to 22.
You can see that, all you have to do is swap red with either green or blue, and you'll evetually get all green, after swapping 28 reds.