That isn't part of the normal JavaScript implementation. JS lives in a sandbox, which means it is totally unaware of anything beyond the scope of the DOM except when the browser chooses to grace it with a bit of information. Opening the find dialog/bar is not one of those.
Going in that direction would start to cross the line of privacy vs invasiveness. If a web page can know what you're doing in your browser, that opens up a massive set of problems.
However, you can know if the web page has lost focus, which includes (among many, many other things of course) launching "Find". For a stupid-simple example, put this at the bottom of your page, after </body>
. (You can be smarter about it by attaching the event after onload):
<script type="text/javascript">
document.onblur = handleBlur;
function handleBlur()
{
//do something
}
</script>