A rope-only handle can actually be made quite firm and solid. But depending on the look you want, you may end up with something that is less solid than you might otherwise prefer. If you like a good solid feel to you handle, you can add a core. A simple wooden dowel is all you need.
If you have 6 strands in your flogger, a core that is the same diameter as your rope is a great choice. The six ropes will arrange themselves neatly around it. If you have more strands, you may need a core that is a little wider.
I typically cut my cores to be 7-8" long. That gives enough for the handle itself, plus a little to extend into the transition knots on either side for additional stability.