About 6 months back, I was struggling with a similar problem. Here are possible solutions:
1.) You are creating a Flash/Ms-Access application for a website.
Flash alone does cannot access the database. An intermediate language is required(like ASP for your purpose).
Asp will get requests for variables from flash and retrieve them from database(ACCESS).
Read flash docs for this. esp the details about object LoadVars.
You can also make use of Flash Remoting if you have the components.
By far it is the best option for high level projects.
2.) You are making desktop application for "offline" usage:
Here yo can either use VB
with flash activex control freely available
or use applications like screenweaver
Hope this info helps...