The general historical accuracy of the Synoptic tradition regarding John the Baptist, including the background to the narrative in Mark 6:14-29 par, is confirmed by the information in Josephus’ Antiquities 18.116-119—the only other contemporary reference to John outside of the Gospels and book of Acts:
Now some of the Jews thought that the destruction of Herod’s army came from God, and that very justly, as a punishment of what he did against John, that was called the Baptist; for Herod slew him, who was a good man, and commanded the Jews to exercise virtue, both as to righteousness toward one another, and piety toward God, and so to come to baptism; for that the washing [with water] would be acceptable to him, if they made use of it, not in order to the putting away [or the remission] of some sins [only], but for the purification of the body: supposing still that the soul was thoroughly purified beforehand by righteousness. Now, when [many] others came in crowds about him, for they were very greatly moved [or pleased] by hearing his words, Herod, who feared lest the great influence John had over the people might put it into his power and inclination to raise a rebellion, (for they seemed ready to do anything he should advise,) thought it best, by putting him to death, to prevent any mischief he might cause, and not bring himself into difficulties, by sparing a man who might make him repent of it when it would be too late. Accordingly he was sent as prisoner, out of Herod’s suspicious temper, to Macherus, the citadel I before mentioned, and was there put to death. Now the Jews had an opinion that the destruction of this army was sent as a punishment upon Herod, and a mark of God’s displeasure to him. (LOEB translation)