In the last month or so, Flutter updated its Web FAQ with a section dedicated to cache concerns:
They outline a few different strategies, including how to force an app download after a new deployment. One thing in particular that may be necessary is to disable the service worker (as described at the end), assuming you don't need PWA functionality. But you may need to try several of these strategies before finding one that works.
Cache busting has been one of our team's pain points with Flutter Web, but it's good to see the Flutter team starting to address this.