Question

Edit: I mixed a.com and b.com in my original post, I’ll try to rephrase stuff correctly:

• A HTML page is loaded from a.com
• The HTML embeds a Flash client from b.com
• HTML contains a Javascript function that makes a connection to a.com, ie the origin of the HTML, not the origin of Flash
• The Flash calls that Javascript function

Question: Do I need to have a crossdomain.xml in a.com?

Answer 1

Please provide more details
and in the meantime take a look at flash parameter :

<param name="allowScriptAccess" value="sameDomain" />

“sameDomain” is the default value
As said in http://kb2.adobe.com/cps/164/tn_16494.html

When AllowScriptAccess is “always”,
the SWF file can communicate with the
HTML page in which it is embedded even
when the SWF file is from a different
domain than the HTML page.