Here is the updated schematic.  All items shown in red are replacements to the original kit.

1. C2 was added to help out the battery when all the LED's are firing.
2. VR1 and VR2 replace the resistors from the kit to provide flash rate and strobe effect (pulse width) adjustments.
3. The 2N2102 transistor is used to drive the bank of LED's.
4. RLED is the current limiting resistor for the UV LED's
5. I show only 1 LED here, but you should wire as many as you need in parallel, each with its own resistor.