Flash Player 10 is over a decade old and contains numerous unpatched security flaws that hackers can exploit to gain control of your computer.
Many third-party "installers" are actually shells for malware, ransomware, or fake antivirus programs that can compromise your Windows XP system.
Adobe and security experts strongly advise against searching for "free downloads" of older Flash versions on third-party sites.
If you need to run legacy Flash content (.SWF files) on a Windows XP 32-bit machine, there are safer, community-maintained alternatives:
Adobe added a "kill switch" to later versions of Flash that prevents them from running content at all after January 12, 2021. Safe Alternatives for Windows XP Users
Finding a legitimate can be challenging because Adobe officially ended support and distribution for all versions of Flash Player on December 31, 2020 . While Flash Player 10 was a standard for Windows XP systems back in its prime, Adobe has since removed all official download links to protect users from severe security vulnerabilities. The Risks of Downloading Flash Player Today