Most people are not even aware that each of the three types of flash player installers come in two different flavors:
(i) one signed with sha256 (which XP considers invalid because it does not know how to authenticate, despite their being OK), which can be downloaded from the links you posted;
(ii) another signed with sha1 (which XP does authenticate as OK), from the links @Bersaglio used to post and which I have posted this time, since he didn't. Those links change with every new version, but are easy to create by hand once the version number of the latest release is known.
However both flavors of installers have the same payload, for each one of the three existing types of flash player.
Now, those who find what I just said confusing or do not know what I'm actually talking about may as well ignore it totally, since it's just a daetail of little importance for most of us, except for those affected by supermegaueberparanoid (me included, in this case) tendencies, and want to validate the installers before use, without having to make use of a Vista+ machine just for that. That's all there is to it,