What voltage rating should capacitor be in this LED driver circuit?
The capacitor cannot charge higher than the 3.3V supply, so a 4V or 6.3V type would be fine. So, probably you're looking at a 5mm diameter part. 

There is nothing limiting the current through the LED other than its own internal resistance and the transistor beta (and a bit of capacitor ESR). I realized that you want a bright flash, but this could be harmful to the LED, the transistor or the capacitor. 

Gain of that particular transistor falls off rapidly above 100mA but you're probably looking at a poorly controlled current of somewhere between 100mA and 200mA given the high gain of the BC847. Specs to look at would be: 


Maximum peak current rating of the LED (should be in the datasheet), and based on a certain length of pulse. 
Maximum RMS current of the capacitor (calculate from repetition rate, peak current and datasheet ripple current rating). Pick one with a relatively high rating such as 250mA or better for long life. 
Transistor heating- assume current is limited by transistor and use repetition rate to calculate mW dissipation and thus heating. 


If it's a hobby one-off and you don't care about longevity, you can just try it and see how long it lasts, of course. The LED is probably the main issue for low rep rates.