I am trying to install version 126.96.36.1997 with no luck. I am running Windows Vista Home Basic Laptop and Mozilla Firefox Browser version 43.0.3. When I try to install, it will download and I get to step 2 of 3 on Flash Player install page. I then click on the download after it finishes downloading and nothing happens after that. I have gone into my downloads folder and clicked "open" and double clicked the download as well, and nothing happens. This is the very first time I've had this problem. I also have Internet Explorer 8 without the S.P. 1 installed on this computer. It is showing that I have Flash Version 7.0.19 installed. I have not found a way to uninstall it. I had restored the hard drive disk just yesterday to "out of the box state". I have not seen any error messages.
Try the offline installers located at the bottom of the page listed under 'still having problems'
If you want the adobe uninstaller for ALL flash player versions, it is located here: Uninstall Flash Player for Windows
Remember that you will have to re-install per browser plugin type, as the Adobe Flash Player Uninstaller will uninstall them ALL. It is important to note that you can have different version numbers here as well because not all browsers and applications use the same plugin remember this. Also just because you went and installed Adobe Flash player in Internet Explorer DOES NOT mean it will be updated or installed for Firefox and vise-versa.
i) NPAPI - This is for Firefox most notably.
ii) ActiveX - Internet Explorer/EDGE(windows10 technically does not use ActiveX plugins)
iii) PPAPI - Opera browser
In addition to Carm01's comment, this is most likely due to Microsoft ending support for SHA1 digital signature. See Microsoft Security Advisory 2880823 for more information. The tech note Installation problems | Flash Player | Windows 7 and earlier also contains information on this and a link to Microsoft's website to update your system to support SHA256 digital signature.