Can a breaker going bad cause GFCI to trip?

I don't see how. What's the problem?

GFI was kicking off, changed it out, no help, finally after trying multiple other things disconnected all but incoming wires, still would not reset! There were a couple times it worked and thought it was fixed but now won't reset at all using either of the GFI's. Have had several instances of other lights in house flickering and one room even staying off then finally coming back on!

I would start looking for intermittent open circuits. A GFI outlet will not reset if there is no power or if there is an open neutral. The flickering and other circuits going off sounds intermittent open circuits to me. The first thing I would do is pull a couple outlets and see if the quick connect holes in the back of the outlet was used to wire the outlets. The quick connect method of wiring is notorious for developing bad connections after a period.