why is the kinetics of oxygen reduction is faster in alkaline than in acidic environment?

Answer 1

You need to provide more information for this question. What is the oxygen combined with (I assume it is not elemental oxygen) and what is the reducing agent? If you need to calculate a reaction rate you need much more data.

In general I would say oxygen (g) reduction is faster in acidic solution due to the prescence of hydronium ions and the lone electron pairs on oxygen molecules. However you need a source of electrons, as reduction is a gain of electrons, and negative hydroxyl ion has an unpaired electtron.