The way reserve leaders learn arts is by the way your Rush acts in combat. If Rush uses Combat Arts, your reserve leaders will learn Combat Arts, if he uses Mystic Arts, your reserve leaders will learn Mystic Arts, if he uses Item Arts your reserve leaders will learn Item Arts. The more Battle Chain you have the faster they learn the arts. This trick also works with raising reserve leader's stats when your BR is already really high, though it will take some effort before results can be seen. A higher Chain will help with increasing EXP gained towards their stats.