The association gets stronger with available evidence if you stay seated a long time in a cramped position, and travel for many hours. The problem is that you are immobile or relatively immobile and, as a result, the return of blood is slowed down and there is some amount of stasis. As of now, there is no scientific evidence that aspirin prevents air-travel related venous thrombosis. There have been people who think taking aspirin would help, because there are many medical conditions where people are given aspirin to prevent thrombosis. But this type of thrombosis is different, because it occurs inside arteries.
Arteries are blood vessels that take blood away from the heart.
Their roles are different from blood vessels called veins. For various reasons, aspirin is good for arterial thrombosis. That's why it's prescribed after heart attacks and some kinds of strokes. But for prevention of venous thrombosis, it is not that effective. In any case, there are no studies that aspirin prevents air-travel related venous thrombosis.