How can I set an API key, which contains equal sign set at Drush site-install?
It looks like there isn't a way to do this, actually. The site installation code splits the string on the '=' and doesn't do any unescaping nor does it look like it would support this. I haven't tried escape()ing the value and then passing it in (so that = would become %3D) but unless you were expecting an escaped value this would probably still not work.

Depending on what you're setting, your best bet might be to do some sort of drush variable-set and set the values after the site install completes.