It used to be (and may still be) that mri_convert can read AFNI HEAD/BRIK files, but cannot write them - hence the "write unsupported" error. You should try your convert function to NIFTI. That said, I'm still fairly sure that a thickness file is a surface that should be converted via mris_convert or the above mentioned mri_surf2vol command.
I also vaguely recall that @SUMA_Make_Spec_FS will do some of the heavy lifting for you and create GIFTI versions of the thickness files and a NIFTI file called lh/rh.ribbon.nii file that may be of use to you.
