There's no direct relationship between Ambien and DVT (deep vein thrombosis), i.e. it's not an adverse effect. The concern is the lack of movement while asleep. If you're lying on a flat-bed seat, that's fine. However, if you're stuck in sardine class, you may be scrunched up with legs in a bent position for hours while you're under the effects of the medication. This is what increases the risk for DVT.

I've heard people taking aspirin before a flight. Aspirin is an effective blood thinner if you're not allergic to aspirin, not prone to stomach problems, and not taking other blood thinners like warfarin.

I caution against taking any prescription sleep medication without being aware of how it effects you personally. For 90% of the population a certain drug may have no adverse effect, but would you want to be that 10%?

Personally I don't take sleep medications on flights. Watching a bad in-flight movie usually does the trick