I'm not sure that a washing machine or dryer or stove can visibly "flicker", but if most of the lights are flickering on many different circuits that's usually the indication that you have loose service feed wires somewhere between the meter base and the panel lugs. You need an electrician to check that out for you.

Why does grounding your light switches make you uneasy? If a ground wire is too short, wire nut on a pigtail so it will reach. Hopefully box fill won't be a problem.

Do they just flicker at random or is it when something is starting up?
Do they go brighter or just dim and come back?

I'd like to know if these are fluorescent lights.

For one, many of the tube-style flouorescent ballasts want the tubes mounted within 1/2" of a grounded metal reflector - and if you ignore this instruction, the results can sometimes be that the light flickers or doesn't start reliably. (of course, sometimes they work fine anyway).

Second, fluorescents respond to low supply voltage in a number of ways, one of which is sometimes flickering.

These are incandescent and halogen lights- no fluorescent. They were flickering at random.

We hopefully figured out the issue tonight. The lights in the house only seemed to flicker after turning on the porch lights. Both lights were on timers, so we swapped them out with standard switches. There is no more flickering.

They were Intermatic EJ500 if anyone is interested (in avoiding them).