Trying to make a current source with an XRP29302 (linear regulator)
Yes it can be used as a constant current generator. With reference to the circuit: -



Take all the ground connections and group them together - this is now going to be the output voltage point for your load and the voltage across R2 (ADJ pin) will cause current regulation when this voltage is 1.24 volts. In other words if R2 is 10 ohms then 0.24 amps flowing into your load will be the current limit. R1 may be chosen to be quite low but the data sheet doesn't appear to say if this can be zero ohms. Maybe an experiment or more digging around will find an answer.

This method isn't limited to this regulator. Here's a 7805 regulator turned current source: -