App Inventor does not offer a feature to get a list of filenames of a directory
a workaround is to call a terminal emulator app using the activity starter and store the result in a file, then read the file using the file component
the statement to execute could be something like this (assuming you want to list all files in directory /mnt/sdcard/Music including all subdirectories)
ls -R /mnt/sdcard/Music > /mnt/sdcard/myResult.txt && exit
Taifun