It's not you, it's us. We don't make Flash Player for Android anymore.
The last working version published for Android is missing a year and a half of security updates at this point, so I would highly recommend against running it.
The details on why Adobe dropped support for Android are here, but yeah, we haven't released an Android Flash Player since late 2012.
There are a few alternatives that you can use to get Flash on your phone. They're mostly cloud-based web browsers, where they run Flash in the cloud and stream the content down to your phone. It works surprisingly well.
A cursory Google search for "Android Browser Flash Player" turns up these options:
Thanks, Jeromie, for taking the time to answer my inquiry, and even moreso
for replying so fast and so thoroughly. I really appreciate it.