Standard channel for Adobe Flash Player updated to 32.0.0.105 on January 8 and confirmed working on Windows XP SP3. 

https://labs.adobe.com/downloads/flashplayer.html

Chrome 45 and newer PPAPI:
https://fpdownload.macromedia.com/pub/labs/flashruntimes/flashplayer/install_flash_player_ppapi.exe

Chrome 44 and older, and Mozilla Firefox (NPAPI):
https://fpdownload.macromedia.com/pub/labs/flashruntimes/flashplayer/install_flash_player.exe

Internet Explorer:
https://fpdownload.macromedia.com/pub/labs/flashruntimes/flashplayer/install_flash_player_ax.exe

Uninstaller:
https://fpdownload.macromedia.com/pub/labs/flashruntimes/flashplayer/uninstall_flash_player.exe