Hi
Interesting! Could you tell us more about the flash drive? How do students "install" it in the PC? Does is assume a particular operating system (like PortableApps)? You know that there is a stand-alone Moodle on a flash-card for Raspberry Pi https://moodlebox.net/ ? In fact I had a similar idea https://discuss.moodlebox.net/d/27-a-pool-of-moodleboxes-an-idea which I didn't follow up.
Technically, the Moodle Mobile App provids the functionality in part. Since there is a Mobile App Desktop too, together they go a long way. One big difference though is the fact that the initiation and the (sporadic) syncing should happen through the Internet.
Doing it yourself has to overcome an obstacle imposed by the way databases work. The database records generated at the sites will conflict, because they are not aware of the data at the other sites.
This topic has been discussed a couple of times in the Hardware and performance forum. Try a forum search.