I am sorry as I would like to help yop, but I can not find your Frank Dickinson in any of my references; Barry County Death Records, Portrait & Biographical Album of Barry and Eaton Michigan (1891) (book); though several persons by this surname are listed in each.
The information that he lived in Grand Rapids may be a clue as to the location of his death record. You stated that you had sent for a DC; did you send it to the Kent County Records Clerk?
The Dickinson names in the Portrait & Biographical Album of Barry and Eaton Michigan (1891) (book); are Daniel page 221, Hiram R. page 270 and Hinman S. page 818. If these are names that you are interested in let me know at by E-Mail email@example.com and I'll transcribe them for you and send them to you by E-Mail.