>I had an LED light fixture installed in my upstairs hallway that worked without issue for a year and a half, before it started flickering beyond use the past week.

Chances are that the electronics are going bad in the fixture if it's flickering badly. Can also show as a repeating on/off cycle.

> I bought 2 new switches and tried both of them. When the new switches were installed, the light would not work at all, not even a flicker. With the old switch installed, I still get the flicker.

Have another look at the connections on the new switches - if they didn't work at all chances are that you messed the connections up rather than a fault in both.

It's possible that you are getting voltage fluctuations because of old wiring but I'd check the above 2 things first.