We shipped Flash Player 10.3 in 2011. Mainstream support for Windows XP ended in 2009. We're not going to do anything to fix this.
More importantly, there are easily several hundred unpatched vulnerabilities that have been addressed by current Flash Player versions. The current version of Flash Player still installs on WinXP.
Your XP machine shouldn't be connected to the Internet at this point. Particularly if you're doing anything remotely sensitive, like accessing banking, using a credit card, sending personal info. If it's a money thing, Mint Linux is free and offers support for secure modern browsers and the underlying encryption and network security that's necessary for using the modern web. Otherwise, you can get a cheap Win10 machine (there are totally workable laptops in the US for $400 that run Win10), or like a Chromebook for $250. You can even find refurbished Macbooks in the hundreds of dollars on Walmart and Amazon, if you don't mind being a few generations behind.
Seriously, it's time to let the WinXP machine go. It's a foothold into your network, and there's just a bunch of automated machinery sitting around on the network that just scans for outdated machines. Popping them and adding them to a botnet (best case) is trivial, and then the machine is a foothold for attacking everything else on your network from behind your router/firewall. If you've airgapped that thing for your WinXP nostaliga machine, I guess, but it's time to move on from actually using that thing to interact with the world. It's a hostile place out there, and WinXP is too pure to exist in this world.