All scripts, flash files and images are loaded once for all at the beginning before the game starts when you have the green bar showing the loading process (24 items)... after that, all the stuff is done by flash locally and the infos exchanged with the server are ridiculous... You can see that by using the network sniffer of firefox before launching the game...
So except momentary slowness that can raise as well on the server or on the Internet, the problem come more often from the general state of the computer and also a corrupted flashplayer installation or a failed upgrade
If other things on your PC are also slower than you think they were before, try first to check your machine for malwares and unneeded gadjets...
If not, you can try this, that I just did with succes, to clean your Flashplayer installation :
I saw a big slowness in the visits and in the fights, a little bit after my last Flashplayer upgrade... after some investigations (into Firefox plugins list), I found that I had 2 different version of Shockwave Flash (the actual 22.0.0.209 and an old 21 one) I was unable to remove or unselect the old one. The 21 version wasn't in the programs list of Windows installer. Deselecting version 21 into Firefox plugins list was also deselecting version 22 so...
I downloaded a FP remover from adobe site :
uninstaller
I closed my browser, launched the remover (that is faster than standard installers)
restarted my browser and went to adobe site to check the result :
check uninstallation
then I downloaded the last Flash player from adobe :
Flash Player (Don't forget to uncheck stupid promotions)
close your browser and launch the installer
After that I retreived my old normal speed when visiting or fighting
NB : because youtube and other videos sites are also using flash to display videos, it's better to close any other tab of your browser with an open video or any complex animation... as well as other flash games