I know it is possible to flush all cache, or to set single file expirations, but I'm curious to know if there's some way to flush a single file via http request;
something like curl -X DELETE www.example.com/js/a_cached_example.js.
Is it possible? How?
It is not possible to do that in 1.8, but it will be possible in 1.9 or from a trunk build, as of https://code.google.com/p/modpagespeed/source/detail?r=4069
It will work pretty much exactly as you predicted if you set the request-method to DELETE in the conf file, though PURGE is what we thought was more common. You will also be able to do that from the admin console (/pagespeed_admin).