I love Polymer too, but if you are like me the parts you like most about Polymer are the beautiful widgets and the ability to create new widgets. Flutter provides that for mobile apps. As someone else said, Polymer itself is just a web implementation of user-defined HTML elements and makes no sense for mobile apps.

As for not wanting to learn Dart, if you are currently developing mobile apps for one platform (say Android) and you want to port your apps to the other platform (say iOS) then unless you already know the languages and libraries used by that other platform (say Swift or Objective-C) then you already have to learn a new language. Wouldn't it be better to learn something like Dart that compiles natively on both platforms? Then you can just write one program. In particular, maintenance is much easier.

(disclaimer, I like Flutter so much I just joined the Flutter team)