Answer
When air is blowing across the top of the chimney on a windy day, this results in an even lower pressure at the top of the chimney. As a result, the gases will flow upward at a faster rate. Therefore, on a windy day, it is easier to get a good draft in the chimney.
Work Step by Step
The draft in the chimney, that is the upward flow of gases, results from both the lower density of the heated air, and from the pressure difference at the bottom of the chimney and the top of the chimney. The bottom of the chimney has a higher pressure than the top of the chimney.
According to the Bernoulli equation, there can be pressure differences depending on the fluid's velocity. A fluid moving quickly has a lower pressure, while a fluid moving slowly has a higher pressure.
When air is blowing across the top of the chimney on a windy day, this results in an even lower pressure at the top of the chimney. As a result, the gases will flow upward at a faster rate. Therefore, on a windy day, it is easier to get a good draft in the chimney.