I have never used flips or new tots wraps, but I have used older tots wraps and the new ones don't look like they are too different in fit / style.
The tots wraps are very stretchy and snug fitting, so could definitely be used to hold an insert / prefold in place IMO esp on a less mobile baby. I don't think they have gussets though (I have seen some with gussets but think they have gone on the newest version), so not sure how good containment would be
I would also be worried that the insert would move around quite a bit if it's not fastened in some way, but then I've never used prefolds / flips so not sure how that works with the system you're using atm.
You can normally pick them up quite cheap preloved, so it's probably worth trying one out (even if its an older version) before you buy new ones.