I'd personally stick with your gut feeling and reject their request for Flash buttons for a few reasons:
- Search engines won't spider through them (essentially hurting the site's ranking).
- Pages take longer to load because Flash adds a lot of overhead on low-powered systems. They won't work at all on things that don't support Flash (read: millions of smart phones).
- Buttons are harder to edit and maintain.
The first two should be justification enough for the client.
StackOverflow is probably a more helpful place for specific help on doing something like that though.