I don't know anything about flickering circuits, but those little fake tealights are pretty cheap and (at least the ones I got) completely self-contained.
I only know this because I wanted a flickering flame effect for the power light on
one of my pedals and got some of those fake tealights. I dissected one, thinking that it would have the circuitry I needed in it, but in fact there was
nothing in there but a weird LED and a resistor. It turns out that the weird LED was doing the flickering all by itself. I wound up taking it out of the pedal because I think it was making noise in there, and the flickering effect wasn't the greatest simulation I've ever seen, but something like that may be another option.
I can't vouch for these in any way, and the "electronics" on Amazon are usually ass, but here's the first example of them them I could find without having to buy the whole tealight:
https://www.amazon.com/EDGELEC-Flickeri ... 73&sr=8-10...although if you do get the tealights, they also come with a rubber flame-shaped cover for the LEDs.