The app uses around 40-45Mb of storage space for both Android and iOS. Content displayed within the app is streamed over the internet and not stored locally unless you've specify downloaded content items for viewing offline, more about this here.
How can I check how much storage space is available on my device?
You can check how much storage space you have available on your device by doing the following:
Go to the device Settings > General > Storage & iCloud Usage > Storage, here you will see how much space is available and currently being used (see below).
Go to the device Settings > More > System Manager > Storage here you will be able to see Used space and Available space (see below).