Actually, no he can't - not unless they agree. Here is the pertinent rule:
"(a) The officers of the Republican National Committee shall consist of:
(1) A chairman and a co-chairman of the opposite sex who shall be elected by the members of the Republican National Committee. ...The chairman or co-chairman may be removed from office only by a two-thirds (2/3) vote of the entire Republican National Committee.
" So unless Trump can get 2/3 of the RNC to go along with him, he can't oust Priebus, and unless he can get a majority of the RNC to go along with him, he can't get his own person installed. Now since Trump has made such a point of insulting and pissing off every member of the RNC, how likely do you think it is that they would want Trump supporters in those spots?
I would think after his two year term is over, he could exert enough pressure and have enough influence in the party to ensure that he is not there.