Most don’t; some might. Whether or not someone is an atheist depends only on whether or not they believe one or more gods exist – no other beliefs are a factor.
Reincarnation is the idea that, after you die, you come back to life, perhaps as another human or perhaps as an animal.
Atheists generally don’t believe in reincarnation for the same reason that they don’t believe in the existence of a god: there is no good evidence for it. Atheists are generally sceptics, and will not accept something as true unless it is proven logically or by good evidence.
Atheists don’t consider ‘memories’ of past lives to be good evidence. Such memories cannot be verified by anyone other than the person who has them. They are also subject to embellishment and in-filling by the imagination.
However, believing in reincarnation doesn’t make someone not an atheist. The only thing that makes someone an atheist is that they don’t believe that one or more gods exist.