Using this tutorial, you will see how to create e-mail button in flash using a little action script code. You can use this button for any web site, and on that way, enable every users to sent e-mail. Let's go!
Step 1
Open a new flash document.
Step 2
Create any button which you like to use for this example. My button looks like this:

Step 3
Take the Selection Tool (V) and click once on the button to select it. Then, go to the Properties Panel (Ctrl+F3) below the stage. On the left side, You will find the Instance name input field there. Call this button "button". See the picture below.

Step 4
Create a new layer above the layer 1 and name it action.
Step 5
Click on the first frame of layer action and go to the Action Script Panel (F9). Then, enter this code inside the actions panel:
var address="example@mail.com";
var caption="Hello";
var message="Hey, how are you? I'm in New York. See ya next week! Bye!"; button.onRelease= function() {
getURL("mailto:"+address+"?Subject=" + caption + "&body=" + message);
}
Test your button, we're done!
Download source file (.fla)