without using the Internet?
You really do not want to avoid using the Internet 
, however if you do you could try any of these untested ways :(:
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possible ways to transfer a file using helper apps or hardware that might be able to be used with App Inventor . The file you transfer will probably have to be a csv file you create from your TinyDB. If you are successful, you will have to load the csv on the other device and load the csv into that device's TinyDB. Some depend on using other apps, others depending on using a particular phone brand. All the solutions are awkward.
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using the Share component to save a csv of the TinyDB and share with the other users.
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copy the TinyDB as a csv file, download it using your USB to a directory in your PC from your device; then use the second device to upload the csv file to the second device using USB and then convert the csv to a Tag in the second device.
Someone else might have other ideas.