It looks like you've downloaded and mounted the DMG and then dragged it to your Applications menu.
Drag the Flash Player from the Applications menu to the Trash.
Eject the Flash Player disks from the left-hand side.
Look in your downloads folder and re-run the installer that you downloaded, or get a new one here:
Double-click the DMG
When the new window opens, double-click the installer icon
Follow the prompts.
Flash Player doesn't install a separate application, it's just a browser-plug in. Once the installation is complete, you should be able to use Flash in Safari.