Say you’re going to the airport. For some reason, as you go through security in the US (as a US citizen), authorities call you for a search. Next, they want to see your phone (for some outrageous reason, just go along with it), and you refuse. They threaten you, so you give the duress password and it erases your phone.
What likely happens to you next?
I’m sure I’m missing so many answers to questions you might have, I’m just curious.
It depends.
If you’re unlucky
Please note that we cannot give any legal advice here. What would actually happen depends on many circumstances and might be completely different for you.
Cops will do whatever they want, legal or not. The only time what’s “legal” actually matters is in court.
That being said, if you’re a US citizen entering the US they’ll probably just get mad at you and eventually let you go. They might keep the phone, or clone the empty phone (lol) before giving it back.
But yeah, who knows? The only way to avoid this is to not bring such devices to the border in the first place, not with fancy PINs.
I don’t know what would happen. What I can tell you is what I would personally do in that situation. In the hypothetical scenario of me getting randomly chosen at an airport for a search I would comply and let them see my phone and any other possessions I may have on me. But I would NOT unlock my phone for them because unless they have proof of me committing an illegal act with that specific device I would demand they get a warrant. I would also take personal joy in giving TSA as much of a headache as possible because I truly believe they are one of the most intrusive agencies out here. But on a more broad spectrum, this is also one of many reasons why people shouldn’t be storing sensitive data on their phones.
Valid points. I guess the takeaway is backup before, wipe all data, and then restore after clearance from cloud?
Evidence of what? A wiped phone? 
What does a duress password PIN login look like? Does it say please wait while a wipe is going on? What does it actually say? Does it look like the first time you boot a fresh phone?
Haven’t tried it yet. I’ve set the duress password, but I haven’t tested what it does.
Maybe but I would recommend some sort of host-side encryption before uploading to a cloud. I wouldn’t just put all my trust into the cloud’s encryption process. Putting everything into zips or tarballs and encrypting them on your own machine first is the best way. Or if you don’t like doing it the old fashion way you could use something like cryptomator.
See this video (not by me) demonstrating duress pin functionality. As you’ll see in the video, the duress feature is not intended to be deniable, and it will be extremely obvious that you have used it.
Also, FYI, you can enter the duress pin/password anytime your device credentials are requested, not just on the login screen (source).
They do not need a warrant, though as a US citizen, they cannot deny you entry. If you do not want to unlock your phone at a border, it should be wiped prior to arrival. It is easy enough to keep a backup in the cloud, which can be restored afterwards.
That would be lovely if it was true. Unfortunately, backup solutions for unrooted Android are all bad and very incomplete. Including Seedvault.