Why one circuit affects other circuits
First of all, are you sure that this 20A circuit is independent of the flickering circuits?  It's not unheard of for someone to wire things in strange ways.
But even if they are different circuits, they still have a common HOT and NEUTRAL back at the panel.  If the power tool creates a heavy load on the circuit that can and often will be &quot;seen&quot; in all other circuits on that leg of the panel.
A couple of suggestions:

Be sure that your outlet, wiring, and circuit breaker connections are all firm and clean.  Loose or corroded connections cause voltage loss and that causes excess current to be drawn by induction or other motor-driven tools.

Check that your tool is in proper working condition.  If it's out of adjustment or needs maintenance, it may be drawing more power than usual.