Here: https://wordpress.org/support/topic/177127#post-886724 you will find a download called swfupload_patch.zip. Replace the files in your WP 2.6.3 installation with the files in this zip and the Flash uploader is remarkably restored to your WP installation. See below:
Admittedly, the button looks a bit wonky, but that’s more of a design issue than anything else. The button is a Flash button which calls the upload method directly in Flash, rather than an HTML button that calls JavaScript that calls Flash to start the upload. It’s not really rocket science. I’m not sure how they implemented the button skins, but I’m sure it could be made to load a few tiny pngs to use as skins, so you could customize it by changing the pngs. But honestly, I could care less what the button looks like in this case – it’s my WordPress admin panel. I’m the only one seeng it.
So yay! I’m going to go upload a whole bunch of random files just to celebrate!