Oh boy I can relate. I fly a lot... flare, no flare... life doesn't wait for your UC.
Pop 2 immodium the night before, and one in the morning.
Then, basically eat light before the flight particularly avoiding ANYTHING that can give you gas, and eat VERY light on the flight itself. 14 hour flight and light eating means you will probably be pretty empty. It's always nice to know there's not that much "on board" if you know what I mean. Also, careful with the sodas they keep handing out-- the carbonation will expand and give you bad gas, which can trigger urgency. Just buy a large bottle of water before you get on the plane.
As for the pooping part, please try not to worry about it during the flight. Long flight means big plane. Big plane means lots of bathrooms. Just bring a change of underwear in your carry on (or pants, if you're feeling really concerned) + wet wipes. I'd rather use the bathroom and let it out than fight it for hours on end. I ALWAYS carry tons of immodium in my pocket for 'insurance'-- even though I full well know that it doesn't work instantly.
The only parts that give me major anxiety these days are the boarding-taxying-takeoff (they will NOT let you use the bathroom during this time, and if you're flying out of NYC for example, you can be taxying for over an hour!), and likewise the 30 mins before landing. Unfortunately, I just have to think about it ("oh no, they're about to tell us to fasten seatbelts, and by the time we land and I can use the bathroom will be at least 45 mins, am I going to have any problems?!) and my stomach will start to cramp.