Why is John (called the Baptist) not considered a prophet of Judaism. Josephus seemed to think well of him. And aside from his relationship with Jesus (in the opinion of Christianity) there is nothing that really makes him a false prophet, is there?
There are several answers to your question.
1. John the Baptist is chronicled in the New Testament, a book which is not regarded as scripture by Judaism. Therefore, any prophetical qualifications attributed to him in the New Testament, while regarded highly by Christians who believe the New Testament to be scripture are of no significance in Judaism.
2. If one believes that what makes John the Baptist a prophet is that he foretold of Jesus’ coming and messiahship, then not believing in Jesus makes John the Baptist a false prophet.
3. Since Josephus was born three years after Jesus supposedly died, and several years after John the Baptist supposedly died, his accounts (if this section is indeed authored by him), are not first hand accounts, and are simply hearsay.