There are two steps with your question, the first one is to retrieve the data from your database, the second is how to format this data and use it in Flash.
As far as retrieving the data is concerned, a common solution is to use PHP.
You will need a PHP script that will query your database, return the content and format it. You should find plenty of tutorials on the net for getting the content from the database. Once you have this content , you will need to give it some form of structure. Personally, since the objective is to use this data in Flash , I tend to create "objects" in PHP which I encode with the JSON format. This is a personal preference, a lot of people use XML. Once the objects are created and encoded , I can then pass the data to Flash. Then again, you should find a lot of tutorials on how to structure the response from the database ,either as XML or JSON.
If you plan to use JSON in Flash, you will need to download this library.
http://github.com/mikechambers/as3corelib
JSON is very easy to use, your objects are formatted as a String and in Flash you simply need to take this String and do
var obj:Object = JSON.decode( jsonString );
This will return an object with all the properties that you've set in PHP. I find that more straightforward than having to go thru all the nodes of an XML.
It's very likely that this object , will be an Array of objects , each object could be a "Show" for instance , with properties such as "date" , "location" , "venue_name" etc... all these would have had to be set in PHP.
Practically, in Flash these objects can be turned into classes ( for instance a Show class and a Calendar class ) which you can then use to display your information an link with one another depending on user interaction.
Check tutorials on
- PHP/Mysql
- PHP objects & json_encode() or PHP XML output
- Basic Object Oriented Programming and classes in Actionscript3
- Flash / PHP communication
There are loads of tutorials on the net covering these subjects.