Hi,
What you're looking for is possible by creating a playlist file. This will contain links to all the songs in the USB drive. You can simply play this file with your favorite media player, and it will automatically play all the linked tracks one after the other.
Making this file manually is very easy but somewhat tedious. Just google 'how to make m3u file'. In a notepad file, you will have to write down the paths to all the songs you want in the playlist and save the file as an 'm3u' file. Now you can simply double click on the m3u file and it will play all the songs listed in the notepad file. Most media players support m3u files and so it should work fine on PC and Mac. However if you want to add or remove songs to the playlist, you will have to edit the file every time.
I can quickly code a custom program that takes all the songs in your USB drive and creates an m3u file automatically. Every time you remove or add songs to the flash drive, you will just need to run this short piece of code and you will get an updated playlist file.
All the information I have provided is free. The program would be chargeable. Please drop me a message if you think this program would be helpful for you. Hope to hear from you soon!