Hi.
A capacitor bank will probably not help for the flicker. Caps will help only if you have a problem with reactive currents and want to compensate for that.
What you need is is a rotating net stabilizer. An syncron motor with high inertia (or whatever you call huge rotation mass) on it's shaft. That way, the syncron motor can provide just enough power to prevent flash. Or at least minimize the flash effect.
That said, if you and your neighbour's houses is connected to the same transformer outpur I'd say it must be a poor transformer. So I think a better idea would be to talk about the issue to your local electrical provider.
Just for beinc curious, How many caps did you use to get that capacity?