How to jailbreak an iPhone on update 9.3.1?

How to jailbreak an iPhone on update 9.3.1? - 1

Can't be done yet, the latest jailbreak is iOS 9.1, that's with Pangu. A 9.3 jailbreak does exist, it just isn't available for the general public, it's just a proof of concept that it can be jailbroken, just waiting on a jailbreak team to do it and release it

Ducky said it all.

I recommend that you watch this guy's YT Channel: iDeviceHelp. I've been following him for 6 years and he makes good videos about iOS. He's usually one of the first to making jailbreak videos, so check his channel often for updates on a 9.3 jailbreak.

You can't.