One way to reduce or eliminate the flickering is to add an electrolytic capacitor to the circuit. If the LEDs are getting AC, you will also need to add a diode or wave bridge (rectifier) in between the AC source and the capacitor. This way the capacitor will charge when the positive voltage is present, and power the LEDs for the 1/60th or 1/120th (if used with a wave bridge) of a second needed. A wave bridge would be preferred, since it will power the LEDs and charge the capacitor when the voltage is + as well as -.
One thing to note is that using this method will raise the voltage slightly, since the 110-120V is RMS, and using a capacitor will bring it closer to the peak voltage, which I believe is about 140-160V.