I went through a period where I was building out an A/V studio where I was returning stuff sometimes twice a week. Never heard a complaint, but I got nervous so I actually reached out to their customer service--"hey, I'm building out this studio, I'm getting a lot of stuff that doesn't fit my needs/doesn't fit what the box says, I don't want to get flagged", the rep put a note in my file, never heard a peep.

It's probably not a discrete number or even heuristic (like number of years you've been in good standing). Rather it's probably another part of their machine learning backend that tracks trends and user behavior as a whole.

But as a guess, if you're a new account, maybe 2 or 3 times. For every year you've been a member, probably 1.5 times that number per year up to some max (let's say, 7).

I returned three smartphones over the course of a few months, because each had some hardware failure. I kept the fourth one. Amazon sent an email asking for details. I guess that behavior flagged me somehow.

There's likely a bunch of factors that go into it. Might even be a score that is updated based on your purchase, return history, length of having a prime membership, amount spent on amazon etc.