I've used a number of solutions for running with both the 6 and 6+. Personally, I do not like armbands or handhelds so my recommendations are belt based.
1. Running Buddy pouch (
http://amzn.com/B00ATIE5ZE). The advantage of this one is that you can use it without a belt in certain applications. However, I used it mostly around a Spibelt endurance and that worked well. Works OK with a phone in the Apple leather case but it is a tight fit.
2. Amphipod large Rapid access pouch on either a Spibelt endurance or fuel belt helium. This is a great setup. Works well the Spibelt endurance (
http://amzn.com/B00DC06PAE) which has a nice pocket for keys and the Amphipod pouch for the phone (
http://amzn.com/B0055Q43XO). For days when some hydration is required the amphipod pouch would be placed on a Fuelbelt helium (the kind with 2 bottles on the back). Works well with the phone in an Apple leather case and maybe slightly larger cases.
3. Using the same belts (Spibelt endurance or FuelBelt) but use a Amphipod SmartView pouch (
http://amzn.com/B00UM9X18W). This pouch slips on a belt just like the rapid access pouch but has a see through side where you can use you phone while it is in the case. Comes in a regular and sumo size. This is a nice belt pouch but can be a little tight if your phone has a case on it.
4. I am currently using a Amphipod pouch belt combo similar to the rapid access pouch and FuelBelt combo but it is all made from Amphipod. Works pretty well for my needs (running with a 6+, bluetooth headphones, some water).
http://www.rei.com/product/883560/amphipod-runlite-xtech-2-plus-hydration-belt.
Finally, I have heard good things about the Flipbelts but my understanding is that like the SpiBelt pockets they are not sweat proof. Here in the south that is a bit of an issue hence why all my recommendations have a neoprene or similar layer that keeps even the heaviest of sweat from soaking through.
Additionally, I generally carry a LokSak waterproof bag in my phone pouch while running just in case it rains or I really need something to keep water away from my phone. These are basically high dollar plastic bags.