How do I make this LED flasher more sensitive?
Replace R3 with lower value - say about 100R or remove R3 (emitter to ground)
 OR 10 uF to 100 uF across R3.

Get a variable resistor / potentiometer.
 Connect it from base to ground. 

Use a value of R1 = pot max value or more. 

Adjust pot.
 Observe.
 Report

What this does is move bias point to an fro around transistor turn on point.
 Lowering or removing R3 increases gain.
 Adding capacitor across it does same thing.

Pot to find best operating point plus lower or bypassed R3 is main "gain".

Driving ... (soon)