I doubt it's freewheel related (though it could be). Freewheel problems usually cause chain spooling forward when coasting (jammed or sticky) or delayed engagement when starting to pedal after coasting (sticky pawls). Certainly flushing and relubing the freewheel mechanism can't hurt.

But I suspect you're looking at a chain problem. There might be a stiff link or two causing the chain to skip. Or possibly there's a worn chain or worn sprockets or both. That's most likely if it skips mostly under hard load vs. more randomly at any load.

I suggest you start by measuring your chain for stretch (lots of links and threads explaining this), and if you still have, measure the prior chain. Then keep track of when it skips because the details will provide critical clues. Does it skip on certain sprockets or chainrings, or randomly on any of them? Does it skip only under load? dors it skip only on large or only on smaller sprockets? Is there any kind of rhythm to the skipping, like once every pedal revolution, more often, or maybe only once every three revolutions?