I submitted my question to support and here’s the answer I got:
I’m glad you’re enjoying Seek. Unfortunately there isn’t a way to sync observations, badges, etc., between devices via the internet. If your new phone runs the same OS as the previous one (eg iOS and iOS) you might be able to transfer apps between them.
I don’t think they understand what I’m asking. I simply need to transfer my Seek observations from one phone to another. It’s the exact same phone. What good is the app that tracks my observations if I have to start over again every time I get a new phone??