Yes, you can be signed in on multiple devices with the same account, across both iOS (iPhone, iPad) and Android operating systems.
Your progress status and vocab list for a given story are linked to your account, so that information will be up-to-date on any device you use.
Since your progress is synced to the cloud (which happens automatically when you're online), we do recommend that you only use one device at a time to avoid inadvertent overlapping or erasure of previous progress.