How to connect Dart to SQLite?
As far as I can tell, dart-sqlite is the only public attempt at SQLite bindings for Dart, but it's out of date. My guess is that it would actually be pretty easy to update the code and get it up-and-running.
web_sql and indexed_db are both for use in the browser, which, as far as I can tell from your question, isn't what you're looking for.
Update: I updated dart-sqlite so that all the tests now pass, at least on my machine. You're definitely venturing into uncharted territory if you use it, but it's a start.