You're using session()->flash(); Which puts data in the session for the current request only, after that you're redirecting (new request) so the flash is gone. If you want to actually store things in the session use:
session(["key" => "value"); or $request->session()->put('key', 'value');
@tim_jespers Your description is not correct. session()->flash();" Data stored in the session using this method will be available immediately and during the subsequent HTTP request". Not Current request only. "To persist your flash data only for the current request, you may use the now method" :
$request-> session()->now('status', 'Task was successful!');