Which operating system is your computer running on and what browser are you using to download Flash Player?
Use this link to troubleshoot Flash Player installation issues on Windows and Mac:
Do you have AVAST antivirus installed? If so, richt click the orange Avast icon in the system tray (where you see the clock) and choose to disable all shields for one hour. Avast has a file scanner which runs whenever you try to install an app and this interferes with the installation process.
If you have a different antivirus app, look for something similar in its Tools or Advanced menu.