Help on (non-working) LM317 constant current circuit

Yes, I agree. It should be labeled 3R9.

Additionally - do you know that you cannot light all three at the same time? If you try, the one with the lowest VF will light and the rest will not or will be dim.

And red will be the lowest voltage drop.

I would also drive those transistors a little harder. 4.3mA IBE for 320mA of ICE is not pushing it very hard into saturation. A little variation in Beta could cause one or more transistor to dissipate a bit more power, and there isn't much room for that in those tiny transistors. In fact, that requires a Beta of 75, but the minimum rated beta for that transistor at 300mA is only 60.

As for measuring the current in operation, connect a 0.1 or 0.01 ohm resistor in series and measure the voltage drop. If you want to see it operate without an LED, at 320mA a 10 ohm resistor will drop 3.2V, about what the LEDs will drop. So stick a 10 ohm 2W or better resistor in there and measure the voltage.

You did use a resistor when connecting to your 3.3V source, right? If not, you might fry the LED.

Of course the output is high with no load connected. It is regulating the current, and with no current draw, the voltage reaches the maximum it is capable of supplying.