Slant Six Oil light coming on — need a new pump?

I would NOT suggest engine flush, I once wiped main bearings with them
If it's badly sludged, and you want to keep the engine, pull the pan and valve cover and clean as much out as possible by hand. After that, maybe use one of those oils that are supposed to clean out dirty engines. Valvoline makes one.
Several times when I was an oil sales rep, I had to handle claims in which a badly sludged engine had solvent introduced into the oil. This loosened up enough sludge to block the pickup. If that happens, it's all done.