As a Flash newbie I found this very confusing and it cost me a couple of hours. Answering my own question here in case anyone has the same problem.
Technically you should be able to do something like this:
<param name="movie" value="movie.swf?param=value" />
<embed src="movie.swf?param=value" ...
Or this:
<PARAM NAME "FlashVars" VALUE="param=value">
<EMBED .... FlashVars="param=value">
Both should create a variable in the _root or _level0 scope called 'param' with the correct value.
These are documented here
However, in my particular version of Flash (CS4, ActionScript 2.0), this didn't work.