In ark mobile, the best way to farm these is using a dire wolf and go clearing lower south cave (80.3° Lat, 53.5° Lon)

Lower south cave have lot of spider and they are low level so a high lv dire wolf should make a quick work

1 cave run will give about 4000-5000 chitin (maybe more using sabertooth)

You can then exist and come back to reset the cave to respawn those creature back quickly and repeat

Yea this is basically how i farm chitin on ark mobile

Enjoy