The irregular flickering of a candle light can be simulated with a simple circuit featuring a small incandescent bulb as a light source.
As you can see from the schematic below, the circuit is constructed with only 4 NPN transistors, the first having the role of a simple noise generator and the remaining three forming a basic low frequency amplifier.
Q1 functions as a classic noise generator, having one of its P-N junctions reverse-polarized. Only the base and emitter is used. The noise signal is routed through a capacitor (C1) into a simple preamplifier made with Q2, then into a Darlington pair constructed with Q3 and Q4.
C2 has the role of eliminating high frequencies, so only slow, observable changes will be amplified.
The luminosity of the light bulb can be adjusted with P1.
The circuit should be fed from a 12V battery or a small wall adaptor and consumes around 300mA.