Imo, you want to avoid "flipping" with hands like 22-77 because there is a decent chance you can be crushed by an overpair. Or basically, you will be in a situation where at "best" you are flipping and at worst you are crushed.
WHen someone shoves you need to look at their position. Late position shoves will be with a wider range of hands, typically, Ax, Kx, 22+
Early position shoves are usually going to be with AT+, KQ, 88+
also depends on average stack size. When M < 15 you can expect a helluva lot more shoving than when M > 20.
Lastly, you want to call shoves when you are fairly confident that your range is ahead of theirs. So its not so much that you are "flipping" but rather that you are ahead of their range.
So if M < 15 and you have AJs or 88 in the SB and an aggro V shoves from the CO and action folds to you, this is a snap call. Its not a "flip" but rather your hand is ahead of V's range.
that is the mindset you need to have in regards to these spots. With the dead money, blinds, and antes in the pot, you are almost always going to be correct in calling in these spots with KJ+, AT+, 88+