So is any PVC-based flip really "safe" for long-term storage since they
all contain some amount of plasticizers?

PVC safety flips are distinguished by the amount of plasticizers they
contain, which is much less than regular soft PVC flips.

Is Mylar the gold standard? How safe are coins in Mylar? Which
commercial brand flips are made from Mylar?

I don't think anybody has seriously studied this. I believe polyester
(Mylar) safety flips are safer than low-plasticizer PVC safety flips.
But I believe the difference is small, perhaps insignificant. Again, I
don't think there's any evidence to back this up, just anecdotal
stories. My own practice is to put the few proof coins I have in
polyester flips (Kointain Saflips) and most of the rest in International
Plastics' low-plasticizer safety flips, sold by among others Jake's
Marketplace and FORVM Ancient Coins. I believe the low-plasticizer
safety flips might be problematic in high-heat, high-humidity
environments, but otherwise they're fine. I've read or heard nothing,
anecdotally, to the contrary. Others like them, I know, but I personally
find the Kointain Saflips ugly, with their striations, sharp corners,
and flimsiness, making the coin/flip package less attractive to look at
than coins in the low-plasticizer safety flips. Again, just my view for
my coins.

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Consumer: http://rg.ancients.info/guide
Connoisseur: http://rg.ancients.info/glom
Counterfeit: http://rg.ancients.info/bogos