Yes, BrowserStack supports testing Flutter apps on Android and iOS devices using Appium's Flutter driver.
We also support Flutter Integration Tests on our platform.
Reference information:
- Integration docs for Appium's Flutter Driver: https://www.browserstack.com/docs/app-automate/appium/test-hybrid-apps/test-flutter-apps
- Flutter Integration docs: https://www.browserstack.com/docs/app-automate/flutter/getting-started