Flutter For Web is there a way to store data?

You can use the SharedPreferences plugin for storing and retrieving persistent simple data. They gave support for the web from version 0.5.4+7

Moor is a reactive persistence data storage library which is built on top of sqlite and is based on indexedDb. This library is compatible with most of web browsers.
You can use the package and see the documentation and example from official link.

Apparently you can use localStorage: https://github.com/flutter/flutter/issues/35116