Hi
Welcome to the forum!
Yes, definitely with a history of taking birth control pills and smoking, you are right in being cautious. Blood clots are generally detected by angiograms and dopplar studies. Some blood clots are painful and some remain for life in a person without causing symptoms. The pain comes due to blockade of a vessel and thus the area beyond does not get blood supply properly and hence has less oxygen.
Clots in heart cause symptoms of heart attack. Those in lungs cause chest pain and breathlessness. Clots in deep veins of arms and legs can cause pain redness and swelling. As caregiver pointed out, they can be asymptomatic too.
As mentioned by Caregiver, move around in the airplane from time to time, flex and relax your limbs both arms and legs, keep moving from time to time in your seat, if possible try to raise your legs from time to time and drink plenty of fluids. Avoid heavy and oily food served on airplanes and choose lighter stuff to eat like a sandwich if possible. Of course if that is not possible, then eat what you get in moderation.
Hope this helps. Please let me know if there is any thing else and do keep me posted. All the best for your flight! Take care!
You ask a very interesting question. Eleven hours is kind of a long time, and you should definitely not be a couch potato for that long. The way to avoid clots is to stay hydrated (lots of fluids) and to stay moving. On an airplane, walk around every thirty minutes or so. There's no hard and fast rule. Flex your arms. Do isometrics. Or take short naps of an hour or so. Then walk around. It wouldn't necessarily hurt unless a coronary artery was blocked.