Miniature-scale "flame" lights do exist, but the limitation is not the size or power of the bulb; it's the power source and wiring that's the problem. Here's a visual that demonstrates the real hurdle to using these with movable 25mm scale miniatures:
Granted that's a full-featured campfire flame simulation kit with features you may be willing to do without. The circuit board handles the "flame flicker" as well the conversion of the suggested 9V power source to a voltage that an LED can accept (typically ~1.7V).
A smaller solution is possible in theory, using just a coin- or button-cell battery and skipping the circuit board. (For a bit more money, you can even get LEDs with built-in flickering effects!) The battery could be mounted under the base of a miniature. The leads would require disguising or drilling a channel through the miniature itself (the latter would be painstaking, or prohibitive on minis with small-diametre arms, but impressive). I'm not aware of any existing kits or props that supply such an arrangement, so it would be an entirely DIY kitbashing project.
In the end though, this would be almost entirely aesthetic. A normal LED will cast light far beyond the scale radius of any in-game light source, and you don't have room for circuitry to moderate its brightness to adjust that downward. Even if you did, the falloff for real light is analogue and wouldn't help to indicate the hard lines between lighting levels that most RPGs use to abstract lighting.