Long time ago QVC sold a shakeable Flashlight that had no batteries just a shakeable generator and a super capacitor. This flashlight uses a 5vdc 1.5a wall wart to charge the capacitors.
To figure out how long it will take to charge the flashlight you use this equation
And for total discharge time
T is time in seconds
Rcurrentlimit is the power resistor used in charging the capacitors in ohms
RLED is the LED resistor in ohms
C is total capacitance in farads
One thing you should know if the capacitors voltage is lower than the supply voltage you should put capacitors in series to increase the voltage rating on the capacitors. Usually you should use 2 capacitors in series and the supply voltage should be no more than capacitors voltage times 2. The diode will drop the voltage by some and also prevent discharging it threw the wall wart