You need to be root to install applications.
On arch/antergos, you usually do “sudo pacman -S <[i:1u0zuuda]application[/i:1u0zuuda]>” - the “sudo” part makes you go root for that single command.
Regarding flash player the best way to reinstall it is by simply running “sudo pacman -S flashplayer”
If you’re still having problems with something related to flash player it probably can’t be fixed since Adobe basically abandoned Linux and the latest flash player v11.2 for it is about 2 years old - perhaps try disabling “hardware acceleration” under the flash settings, you can do this by watching a youtube video, right click the video, click settings and untick the hardware acceleration box.
If you’re using Chrome, however, it comes bundled with the latest flash plugin v12.0. To install Chrome you can’t use the “pacman” command because it isn’t in the official repositories. You’ll have to use “yaourt” so just run
yaourt -S google-chrome
Notice that i’m not using “sudo” with yaourt because it asks later for the password so it’s not required.