FUE transplant hairs very coarse and kinky! Is this something that is likely to change?

There is something that is difficult to manage. It does occur and unfortunately it is unlikely to improve drastically. You can try to improve hair health with vitamins like Follicueticals MD. See if you get a change. 

I have seen a few cases where texture changes produced kinky hair. This has been permanent and when I repeated the hair transplant in these few patients, the second hair transplant became kinky also