We've just released a new beta that adds the ability to import mbtiles from device!
We had one surprise along the way which is that we can't easily filter by file extension so we can't show only mbtiles files in the file picker. For now, all files can be selected but any that are not mbtiles will be ignored without feedback. We'll work on adding that feedback.
You should be able to add multiple mbtiles at once but the file picker interface to do so will depend on your device. Generally you will need to tap the icon for the file, not the filename.
We haven't added deletion yet and will be working on that next week. If you have any other feedback on the functionality, we'd love to hear it.