Using the unforked version of Flutter for web:
flutter channel master
flutter upgrade --force
flutter create web .
flutter run (just to verify in chrome)
flutter build web

Works in Chrome and Firefox, but Safari is a blank white window. The Safari JavaScript console shows a bunch of errors.

After removing the references to Cupertino icons and fonts, it loads in Safari. Specifically,

• Remove all references to Cupertino in
  • build/web/assets/AssetManifest.json
  • build/web/assets/FontManifest.json
• Delete build/web/assets/packages/cupertino_icons/assets/CupertinoIcons.ttf