You don't need an amp for JH16 with AK120. At least not for the main purpose of using an amp, that is to boost signal for difficult to drive headphones. JH16 is pretty sensitive and don't need an amp for that purpose.
Some people will tell you that different amps sound different and to some extent it's true. There are many technical reasons for these differences. Look up high output impedance and high sensitivity low impedance headphones and you will get a different perspective.
However, if you like how JH16 sound with AK120 I would suggest to read more about the subjects mentioned above before you start looking for an amp. Unless you are willing to invest time it will be futile and senseless to ask for an amp recommendation for JH16.