Is it possible to get a transparent (not white) background for the flash charts when I paste into my web page?

You can easily set transparent background to Flash Charts Pro:

Using Dreamweaver

Follow the below steps, and Dreamweaver will insert the correct HTML code automatically.

1.    In Dreamweaver, insert the Flash movie into an HTML page.
2.    Select the Flash movie in the Design View.
3.    In the Properties panel, choose Parameters.
4.    For the Parameter, enter "wmode" (without quotes). For the Value, enter "transparent".
5.    Save the document. The HTML page is complete.
   

Editing HTML code manually

To edit an existing HTML page, add the WMODE parameters to the HTML code.

1. Add the following parameter to the OBJECT tag:
   
   <param name="wmode" value="transparent">
2. Add the following parameter to the EMBED tag:
   
   wmode="transparent"
3. If you use Active Content Publishing script (AC_RunActiveContent.js) to show charts, you need also to add 'wmode','transparent' parameters to it.