How does earth maintain a constant level of oxygen?

It doesn’t! the oxygen level of the planet has varied quite dramatically in the last 500 million years ago; as the climate cooled and the land plants died off, oxygen level fell to as low as 12 percent by the beginning of the triassic. Back then, the air at sea level would have felt thinner than at the top of the Alps today.

Burning fossil fuels has reduced oxygen levels very slightly  - about 0.057 percent over the last 30 years. Deforestation only has a small effect because when rainforest is cut down, other plants are usually grown in its place. But it’s marine plankton, rather than trees, that produces about 70 percent of atmospheric oxygen. Global warming will have a significant impact on plankton, which is a much more serious threat to oxygen levels.