How should I set up bypass capacitors for candle flicker LEDs?
All batteries have an internal resistance.  That tends to increase as the battery runs down, especially for alkaline and zinc-carbon ones.  So using thicker wires will make little difference.
A single large capacitor across the power lines is likely to be more effective than small decoupling capacitors.  Try tens to hundreds of microfarads if you have the space in your project.