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:

https://storage.googleapis.com/flutter_infra_release/releases/stable/linux/flutter_linux_3.24.2-stable.tar.xz

 

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.