First each xbox is married to a specific drive. That drives key has to match the xbox 360 it is paired with or you will get a play dvd error. Secondly a retail console can't play games without discs because they can't run XEX files straight from the console
The flashed drive has nothing to do with playing games without a disc. You can have a jtag without a flashed drive and play games without a disc from an external hard drive. You dont even need a disc drive at all to do this on a jtag.
You can get someone to put the flashed drive in your normal xbox. They would just need to change the drive keys so they match and you will be able to play burned games. But there is a risk that you will get banned.