There are several ways to get the driving distance.
-This tutorial explains how to get the driving distance using App Inventor’s Navigate control HOW TO: Use the Navigate control This provides reasonable driving distance estimation (the basic data is provided by volunteers and is not always precisely accurate).
You can also use other methods
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Use an ActivityStarter and intents to open Google’s Navigator app. This link provides basic information https://groups.google.com/forum/#!msg/mitappinventortest/3d7bFyGM508/pNsqAb9hBQAJ
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This advice HOW TO use the new Map Control to plot a route on a map and post driving distance and time for that path. is useful too.
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Again a different way is OpenStreetMap without the Map Component
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And if you are experienced with JSON and willing to get a Google Map API, you can use the Google Directions API . This is the most accurate, up to date information provided from Google’s databases.
Is this what you want to do?
Regards,
Steve