Try this first:
http://mashable.com/2014/01/31/gmail-slow/
This might be worth a try, but flash is not vital for Gmail, however chat and video use it and possibly the new mail sound. It is integrated in it however.
In the URL bar type in chrome://plugins
Expand the page in the top right "Details" and look for Adobe Flash Player, let me know what you have there. Its just a hunch as pepflashplayer.dll has been all over the tech forums as having issues in Chrome, not sure if this would tie into Gmail but its worth a look.
If you have two flash players, disable the one using the pepflashplayer.dll, and restart your browser, check your task manager to make sure all instances of Chrome are no longer running, sometimes addons hang a session.
Also make sure at the bottom of the flash player there is a checkbox for "always allowed" which I would have checked, it stops you from having to approve pages for using flash.