It's possible to use Flarum without using the command line, but it's nice to have command line access in case things ever go wrong and require manual intervention.
You can download Flarum as ZIP with the extension manager and do everything through the extension manager, while keeping SSH access as a backup.
It's probably a good idea to familiarize yourself with how to execute the php flarum info command over the SSH option your host provides. This can be useful in the future, as any command you might need to manually execute in the future would involve the exact same steps.
Having SSH but not using it is a much better option than choosing a host without SSH and finding yourself in a situation where it's needed to quickly sort out a problem.