Why B-52 engines produce lots of smoke only during take-off?
There are a few reasons.

The first is that the engines run more efficiently when the aircraft is moving. As the aircraft moves faster, it's easier for it to get more air into the engine, which helps it run more efficiently.

The second reason is even simpler: like most aircraft a B-52 only rarely runs at full throttle. Most of the time that it's cruising, the throttles are backed off to just overcome the drag and maintain the current speed and altitude (though flying at terrain avoidance level is a rather different story).

The last reason is that the larger amount of smoke is largely an illusion. When the aircraft is moving, it's actually still generating close to the same amount of smoke. We're seeing the smoke from running the engines at full throttle for roughly a minute. During one minute of normal flight, it would generate somewhere close to the same amount of smoke--but instead of being concentrated in the 1 mile or so that we see here, it would be spread across something like 10 miles of sky. In addition, at altitude, you're a lot more likely to have much stronger winds, so exhaust from a minute ago will be relatively widely dispersed, rendering it much less visible than we see here (with air that looks like it's almost perfectly still).