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Take a look at the settings file -- <background> node. Try the <alpha> and <border_alpha> settings.
<background> <!-- background -->
<color/> <!-- [#444444] (hex color code) -->
<alpha/> <!--  (0 - 100) use 0 if you are using custom swf or jpg for background -->
<border_color/> <!-- [#000000] (hex color code) -->
<border_alpha/> <!--  (0 - 100) -->
You should set the alpha values to "0" to make the background transparent. If that's not working, quemm may need to offer some advice.
It's not enough to disable amMap's background by setting it's alpha to zero. You also need to make your Flash object transparent by setting following parameter: