I don't have a good answer. You might have luck on StackOverflow. If you ask on StackOverflow then you may want to cross-post that SO question with the Flutter team to see if they have an answer.

The only thing I can think for you to do is manually instruct the IME to capitalize the keyboard. I'm not sure which API can do that. But one thing to keep in mind is that this exact same problem should exist for Android and iOS without Flutter, so you might want to see how Android and iOS apps deal with this issue.