for cheap oil flushing I use whatever is left over from prev oil changes and use it as a flushing oil. And if I don't have enough qty to do that or the leftover oil is too precious for that purpose I buy the Gulf Western 20w50 4L oil from supercheap auto for $9.95 and use that instead.

I only use flushing oil after a dose of solvent based flush additive eg Nulon engine flush to get rid of any left over flush additive trace as it's very aggressive and I won't want any hanging around the engine till the next oil drain. If the engine wasnt really dirty ie sludged up and could do with a bit of a clean I would use a good old fashion diesel oil such as Castrol RX super 15W40 and run that for say 2000-3000km or even till the next oil change at 5000km.