Hi Pavs, yes, you can move the Flarum container across servers, providers and any Linux OS i.e. Fedora, CentOS, Debian, Arch, Ubuntu etc with the app and your data intact. That's one of the big advantages of containers.
We use Debian Wheezy for our 64 bit containers. Alpine Linux 64 bit is an additional option for some of the apps. For 32 bit containers we use Ubuntu Precise. Though we are going to stop providing 32 bit containers. You can run these containers on any Linux OS and move them around.
For instance suppose you are hosting on your own server, and want to move to a cloud provider, simply zip the Flarum container and move it to the new server. Similarly suppose you don't like your cloud or VPS provider anymore, again simply zip your Flarum container and move to another provider. So you are not stuck to any provider, server or a specific variant of Linux.