for install flutter on linux desktop on x86 you should first install last flutter framework
to install it you can see this page
https://docs.flutter.dev/get-started/install/linux/desktop
and download latest version. in this time current version can be download by this link:
after that extract it and add the path to PATH variable. to check every thing is work you can check flutter doctor command.
and also to make a simple first test application you can use flutter create my_app
and then cd to my_app dir and type flutter run
command to run the application.