First thing to note is Q1 & Q2 form two 0.7v constant voltages, therefore the voltage across R2 as part of the divider with R1 should be greater than 0.7v otherwise Q1 isn't doing it's job.
So 3 - 0.7 = 2.3v across r1 + r2. I = V/R = 2.3 / 1250 = 1.8mA, voltage across r2 = IR = 1.8mA * 500 = 0.92v.
That should be ok - except we really should take into account the current used by Q3.
So Q3 is just a constant voltage source. The output voltage will be the input - 0.7v (voltage drop across emitter/base), so R2 should be set to about at Q3's base.
The maximum collector current is equal to the base current x the transistor gain. DC current gain is listed as 100-300, so if we take the bottom number then to get 300mA out you'd need 3mA into the base...
However we can see that the max current flowing through the R1+R2+Q1+Q2 chain is 1.8mA and that doesn't include anything we need for the base current.
You can tell if the transistor is fully switched on by measuring the voltage across it's collector and emitter, therefore if you set it up for your max current and measure the voltage across Q2 C/E then it should be close to zero, if not the transistor base current isn't enough to switch it fully on.
So basically you need to find 3mA for Q3's base and this needs to be taken in such a way that the voltage across R2 doesn't fall below 0.7v (say 0.8-0.9 to be on the safe side).
If we double the current flowing through R1 to give us 6mA then there's 1.4 dropped across Q1+Q2 so R1 = V/I = 1.6 / 6mA = 266 ohms, call it 220...
Calulate R2 such that half the current flows through it, so 3mA across 0.7v is 233 ohms. (Could use a 100 ohm pot here with a couple of resistors either side to make it up to say 200 or so, just make sure the range is in the right place).
So with R1 = 220, R2 = 200 then current into Q3 base should be good for 3mA or so, with a transistor gain of 100 that should allow the transistor to switch fully on, providing then that R3 (and R6 if you're using it) will allow 300mA to flow then it should work...
R3+R6 are mainly current limiters, they should be chosen to give slightly more current than you need when across the supply (3v).
Hope that makes sense, I've typed it in as I go along...