My front door frame doesn't appear to support installing a storm door; is there anything I can do?
You dont state what your problem is.  You can install the door to the outside of the door frame. It looks like the top sticks out farther than the sides so you either have to add a board the thickness of the distance to the outside of the side frame. If you need more room for the frame flange at the top you can add a 1x2 board to the top of the door . With the thick door frame the bottom of the screen door may not hit something so you will have to look at that. 

Installing a screen door is not an easy project even on a standard door. Especially the first time so if you're doubting yourself you might want to hire someone.