Could the Van Allen belts actually interfere with the Earth's magnetic fields?

The Van Allen Belts are there because of the Earth's magnetic field, it traps the particles that comprise the belts.

Maybe by grounding the belts, the magnetic field would be strengthened.

In a certain sense, it would. The Earth's magnetic field is the result of a net electric current moving in a circular path in the mantle. The current from the belts flows in the opposite direction reducing the dipole moment of the Earth's magnetosphere. The effect isn't large but yes, it does lessen the total dipole moment of the magnetosphere.

I know that electronics are harmed by static buildup, maybe the magnetic fields are too


Taking another look at this question, do you understand why it's gibberish? Are magnetic fields made out of micron sized junctions of silicon? Clearly not. Physics classes are fun.

Could the belts building up to critical levels be the cause of the Earth's field flipping every so often?

Not necessary at all. It could have a weak dynamic effect but it doesn't drive the chaotic (flipping) nature of the geodynamo.