Know therefore that I shall provide for you all in common what is for your good, and particularly for thyself what shall make thee famous; for that child, out of dread of whose nativity the Egyptians have doomed the Israelite children to destruction, shall be this child of thine, and shall be concealed from those who watch to destroy him: and when he is brought up in a surprising way, he shall deliver the Hebrew nation from the distress they are under from the Egyptians. His memory shall be famous while the world lasts; and this not only among the Hebrews, but foreigners also:—all which shall be the effect of my favor to thee, and to thy posterity. He shall also have such a brother, that he shall himself obtain my priesthood, and his posterity shall have it after him to the end of the world.

So we have the slaughter of innocents as an attempt to kill the “chosen one,” and we have the divine visitation. Both of these are in Matthew’s birth narrative, but neither are in the Exodus version of Moses’ birth.

Antiquities was written around 93 CE, in about the middle of the range in which Matthew’s gospel is believed to have been written. It’s possible that the author of Matthew had access, but it seems more likely that they were simply both drinking from the same well of Jewish tradition.