NPN LED variable resistor
A few potential problems:


Low resistance potentiometers are not a good idea, unless you pay $$$
You've forgotten saturation voltage of the transistor (perhaps 0.2V)
Base current is likely insufficient to saturate the switching transistor
A 100mA current surge may cause problems for a feeble +5V DC supply.


That transistor consumes 0.2V of your 5V supply when saturated. To saturate that transistor, 10mA base current should be available, if 100mA collector current flows.

The calculation for collector resistor, for 100mA current now becomes \$ (5 - 0.2 - 2.7)\over{0.1}\$. A 20 ohm resistor might be right.

The calculation for base resistor involves the transistor's base-emitter junction voltage around 0.7V. Fairchild's data sheet suggests it would be about 0.86V @ 25C, for a base current of 10mA. If you were to drive the base from a very stiff 5V logic signal, base resistance would be \$(5 - 0.86)\over{0.01}\$. That's 414 ohms. However, logic gates are not infinitely stiff suppliers of current, so you'll need to reduce this resistance.

Finally, the +5V supply surge current: A large-value capacitor placed close to the 20 ohm resistor, and close to the transistor's emitter may help to keep surge current from disturbing nearby logic run from the same supply.



Your base drive FLASH suggests a momentary pulse. Your transistor may survive a short current pulse without overheating, were it to be biased into non-saturation. This scenario opens up the possibility of controlling LED current by varying base resistance. A fixed base resistor in series with a potentiometer might be appropriate, if current accuracy was not an issue.
If FLASH lasts too long, the un-saturated transistor may flash instead of the LED.