Any of the rivers in N. FL. Suwanne(and feeding creeks)(best site is overlooking the big shoals), Okefenokee(all are good), Cumberland(brickhill Bluff), St. marys(at the horseshoe) can be fun in high water. PM if you want any more details. I realize this is 2 months late.
Edit: I spent 3 years in N.FL paddling every weekend. It has some of the best flat water spots. I STRONGLY recommend this book. It doesn't have everything but its a great jumping off point and will ensure that you get the right spots for what you want. WELL WORTH THE MONEY.
I paddle a good bit. I'd strongly recommend buying the book in the link below. It's $13 but is an excellent jumping off point and well worth the money at twice the price. There's also the state paddling trails but I refer to the book more often than I do that website. You'll exponentially enjoy your time on the water if you set up shuttles for rivers(i.e. a friend).
14 miles seems about right. (Edit2: Are you solo canoeing? Kayaking?) It really depends on flow, gradient, obstructions, fuck off time etc. The Choctawhatchee River is a sizable river so you shouldn't have to worry about many obstructions and I don't think there are any rapids or anything like that in that area (only substantial ones I can think of are on the Aucilla and Suwannee). There's a great book called Canoeing and Kayaking Florida that I would recommend you check out. I would also point you to FDEP's paddling guide for the river. You can check out all the paddling guides for other rivers here.
I've never paddled the Choctawhatchee but it looks like on google earth that sand banks are abundant, as a solo I would target these towards the end of your day as camp sites if the water level is right. It is legal to camp on floodplain (which beaches would be in) but don't argue if someone comes up and asks why you're on their land just tell them you will be on your way. (This has never once happened to me in my many years of paddling Florida's rivers.)
I will also say, while I haven't paddled this river, I have been to Morrison Spring. You are not going to want to miss that if that's part of your paddle. Make sure you allocate some time to hang there.
I can talk all day about paddling in Florida so if you have any more questions I'd be happy to help.
Edit to add "See this trail" link from FDEP: http://fdep.maps.arcgis.com/apps/MapTour/index.html?appid=d1b432eb3ecf4c9f81c0e7a3e3f8c307