App inventor does not have a native way to directly use kml files with OpenStreetMap tiles. Why not try this tutorial (already mentioned by Taifun) or use SAF? you can not merely copy kml/gpx files into the Documents folder and expect them to be usable with the the compiled app . Usable files must be created with the compiled app.
This is what is available at the moment. If you want to do this another way you might have to write your own extension to use your kml file. This is primarily because Google security restricts how an app can use files that the app itself did not create.
See KML - OpenStreetMap Wiki the section KML data into OSM.