There are not so many instruction methods for playing the Jew's harp. I know the following ones:
A French disk "Guimbarde ... Instrument de parole" - Stephane Voisin. It is dedicated to playing in a "Radgastan style". This disk contains audio tracks of exercises which explain this difficult technique. A booklet in French is attached to the disk. The disk can be bought here
СD "The Yakut khomus World" by Ivan Alekseev contains 14 basic ways of playing the Yakut khomus and 8 music compositions.
CD "Altai Khomus- the first meeting". The Russian and English languages. The blacksmith of Altai khomuses Vladimir Potkin tells how to choose the instrument, how to keep it, how to breathe correctly. The disk is supplemented by a master class of Altai musician Nogon Shumarov.