Adobe's last release of Flash Player for PPC Macs was in November, 2010 with release 10.1.102.64 Subsequent releases are for Intel based Macs only.
To check your installed version of FlashPlayer - http://www.adobe.com/software/flash/about
Read this whole post before proceeding. You have to follow steps precisely and there is mention of an alternative version of Flashplayer at the end that some have decided to try.
To update you should download:
Flash uninstaller: http://helpx.adobe.com/flash-player/kb/uninstall-flash-player-mac-os.html Make sure you get the right one.
Flash installer 10.1.102.64 http://fpdownload.macromedia.com/get/flashplayer/installers/archive/fp_10.1.102. 64_and_9.0.289.0_archive.zip Open the archive to reveal yet more archives and multiple files. Select: flashplayer10_1r102_64_ub_mac.dmg
1) Run Disk Utility and verify your hard drive. If the hard drive reports errors then it will need repairing first (another topic). If it verifies, run Disk Utility's repair permissions.
2) Back up your hard drive, ideally to a bootable clone. A bootable clone will allow you to restore your hard drive to its original state should something go wrong.
3) Quit all applications to ensure nothing is actively using Flash. You can even do the next step while booted to Safe Mode to make sure.
Mac OS X: Starting up in Safe Mode - http://support.apple.com/kb/HT1455
What is Safe Boot, Safe Mode? (Mac OS X) - http://support.apple.com/kb/HT1564
4) Run the uninstaller application. Adobe says, "Adobe recommends that you restart your computer before you install a different version of the player."
5) Run the installer application from the .dmg file you got from the second download.
6) Use Disk Utility to repair permissions on your computer. This is important when installing anything from Adobe.
7) Restart your computer.
Adobe installs things all over your computer. Simply dragging a file or two to the trash won't ensure you have uninstalled all old file components.
Comments about Flash and Shockwave. http://discussions.apple.com/thread.jspa?threadID=2769507
Flash player 11.1 hack on PowerPC - https://discussions.apple.com/message/16990862 - this gets FP to tell web sites you are running a newer version than you really are. This gets around web sites that don't really need a new version but think they know best. If they really do require it then this hack doesn't work.
Flash Player version 10.1.102.64 is the last version available to PPC Mac users. However, this Flash version won't work for many videos on Facebook, YouTube and other sites. Adobe's latest version, 10.2.x or later, is only for Intel Macs. Adobe will not provide a newer Flash version for PPC Macs.
The message requesting that you download Adobe Flash Player takes you to Flash Player requiring an Intel processor. Doesn't work on a PowerPC processor. I found a hack, installed it & it works with Firefox, TenFourFox & Safari.
Download this http://www.steelbin.com/FPforFBPPC.zip to your desktop, unzip it, and replace the current Flash Player plug-in which is in your main/Library/Internet Plug-Ins folder, (not the user Library). Save the old one just in case this one doesn't work.
Hack Allows PowerPC Macs to Access Flash 11 Content