Lawdog,
what you call flipping today, we called "Dabbling" back in the late fifties/early sixtys. We would flip a gig/worm/spinner bait around the edge of a brush pile, dock, or other cover. If you didn't get a hit, then you would flip right in the middle and kinda yo-yo the bait. In those days the rods were custom made. (Some even used cane poles) Reels made no difference, they were just there to hold the extra line, normally 17-30 pound test depending on time of year and where you were fishing. The reel wasn't used to recover the line and bring the fish in, this was accomplished by pulling the line from the first guide to the handle where you were holding the rod, then repeated as often as necessary. When the fish was finally boated, you had a wad of line pretty much like a fly fisherman.
That's your history lesson for today, now to try to answer your question. I personally think the rod is most important in flipping, it has to have the backbone to allow you to horse a big fish out of cover. I would prefer a one piece 6 1/2-7 foot rod. I like one stiff enough that I can use it for a pool cue if I decide to quit fishing. don't buy one with a pistol grip handle. A long straight handle with the reel seat in the middle of the handle or forward of center handle is best. Thats for leverage and balance. I recommend the smallest reel that is capable of handling the size line (s) you will be using. Something like the old ABU 500. There are several others on the market today in that size. Remember, you are flipping, not casting, 25-30 yards of line is enough on the reel. On some larger reels you may need to use a filler line and then tie your actual fishing line on to fill the reel for better flipping.
Hope that helps.