I bought a recorder that advertises Flute Master but there’s no license inside.

Some recorders only contain a reference to Flute Master (and the QR code to our website), so you know the app exists and can teach you to play the recorder. These recorders do not include a license to actually unlock the full game.

Unless the package states that a license is included, as is the case with bundles from Voggenreiter and some from Yamaha, the bundle does not include a license.

The license in any case is functionally equivalent to a purchase from one of the online stores such as Google Play, App Store, Microsoft Store and Steam (for the respective operating systems), which can be made from within the game itself. The advantage of having a license is that it can be used on multiple devices and different operating systems, which is not the case with purchases from the online stores.