Hi,
Google is littered with a cacophony of confusion about how to view flash on Firefox in Linux going back 2 years.

Here's the Readers' Digest Executive Summary:
For Suse 11.1 with Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv:1.9.0.6) Gecko/2009012700 SUSE/3.0.6-0.1.2 Firefox/3.0.6 (latest as of 2009-03-11)

Goto http://labs.adobe.com/downloads/flashplayer10.html
Click on: "Download 64-bit Plugin for Linux" link.
Downloads libflashplayer-10.0.22.87.linux-x86_64.so.tar.gz
Stash it somewhere and cd there.
tar -zxvf libflashplayer-10.0.22.87.linux-x86_64.so.tar.gz
su to root
cp libflashplayer.so /usr/lib64/firefox/libflashplayer.so
cp libflashplayer.so /usr/lib64/browser-plugins/libflashplayer.so

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And now, the snide commentary:

When I just copied it to /usr/lib64/firefox, it got rid of the "you don't have the correct version... click here" dead end url. But, I just got a black window where the flash should have been.

The browser-plugins cp command gives me a working flash player although, even with a Bunyanesque video card, a Herculean CPU, megabit+ downloads and scads of DDR3, it is still horribly choppy at full screen, 2560x1600 resolution.

Thanks to the trolls at Adope (microsoft Jr.) for taking so long to make such a crappy decoder for their dreaded, proprietary format and for making the install process so abundantly nebulous.

Perhaps they could learn from the beneficent geniuses at ATI how to properly install drivers like ATI does the 64 bit Linux FGLRX video driver.

Death to proprietary formats,

BrianP

Well that (fglrx) can be a real pain, and is to some, so I hope they don't actually try to learn anything from that. I don't say much about the quality or performance of Adobe flash, except that it makes most sites function like a piece of crap, but it's installation is about the easiest one around---copy a single file to a single directory, or in your case two (I've always gotten away with just one). That's what the "installation" basically is, copying files to filesystem; at least you don't have to compile anything, or mess around with registry of any kind

The other possibility of installation is to copy the file to a similar plugins directory of a regular user (inside the home directory of that user); this does not require root privileges, so non-admins can usually do that too, and on the other hand adds the plugin for that user only, not for everyone.