Mac OS Mojave Downloads

Hi!

I have recently been having issues with my MacBook Pro. I try to download apps such as Adobe Flash-player or Google Chrome from safari, although afterwards, when I try to open the application, I get a message saying ... " “install_flash_player_osx.dmg” is damaged and can’t be opened. You should move it to the Trash. ". When I attempt to switch the settings in System Preferences under "Allow apps downloaded from: ", I switch it from "App Store" ...to... "App Store and Identified developers" . Then, when I go back onto System Preferences, it has automatically switched back to only allowing downloads to come from the option of " App Store". ..... I have done a lot of research and watched quite a few videos on this problem and still haven't been able to figure it out. Please help !!

Thanks!