Nattokinase/Vit E & There is significant risk of blood clots in the legs on long flights, which can travel to the lungs. Walking some every hour or two should help.Drink lots of fluids.Wobenzym, vitalzym, nattokinase & lumbrokinase are the most effective natural blood thinners (any one of these is adequate). Other supplements that prevent clots include vitamin e, garlic, ginger and turmeric/curcumin. Have a good trip!
Compression stocking. The best 'natural' protection against DVTs on long flights is to wear appropriately fitted compression stockings (below-knee) to prevent clots forming in the legs, which can in turn reduce the risk of PEs. I don't recommend natural remedies to thin the blood, as it is difficult for you to safely get the dose right when taking herbal supplements and you could bleed to death.
Natural prevention. Unfortunately there aren't any natural products that prevent blood clots. Except of course aspirin (made from tree bark), but likely not appropriate here. The best thing is to make sure you get up every couple of hours and walk up and down the aisle for 5-10 minutes. If you have a history of blood clots, you should talk to your doctor before making the trip. They may want to try other prevention. .
See your doctor . Aspirin is probably the most natural product that has actually been tested for this purpose. However taking precautions such as giving up smoking if you are a smoker and moving around the cabin is probably the best approach. If yiu are worried, especially if you have a family or personal history of clots then you should visit your family doctor for advice.