Question on LED usage for constant current LED driver
I think you're looking for this:

Figure 1. This table tells us that the supply voltage needs to be at least 1.2 V higher than that required by the LED(s).

Figure 2. The internal schematic tells us why.

The resistor on the left draws current through the two diodes. It's probably a low current so each diode will drop 0.5 to 0.6 V, I expect, giving a total drop of 1.2 V. The voltage at the IOUT pin will be about the same amount lower than that of the +VS pin.


From the comments:

So if the voltage on Iout is the input voltage minus the drop of 1.2v is still around ~10v, could this damage the 3.3v LED, or will the constant current prevent this?

The whole purpose of the chip is to act as a current limiter. If the current increases then the voltage drop across the emitter resistor will increase and the transistor will start to turn off (since its base is held at a constant voltage).
You do have to watch out for power dissipation in the chip so let's look at that.

Figure 3. The absolute maximum power rating of the chip.
The absolute maximum power dissipation is given as 330 mW. For reliability we could aim for 200 mW operation. The device passes 20 mA so that means that the maximum voltage across it is \$ V = \frac P I = \frac {200m}{20m} = 10 \ \text V \$. With a 3.3 V LED that allows you to operate from supplies up to 13.3 V.
Don't forget that you can have multiple LEDs in series. This is more efficient for component count and energy use and heat dissipation.