Contradiction with Numbers 12:6
Contradicts by specifying that God speaks through direct visions and dreams, whereas Luke 3:2 refers to the word of God coming to John as a proclamation.
Numbers 12:6: And he said, Hear now my words: If there be a prophet among you, [I] the LORD will make myself known unto him in a vision, [and] will speak unto him in a dream.
Contradiction with Jeremiah 1:4
This verse describes the word of the Lord coming directly to Jeremiah, which might contradict the method implied in Luke 3:2.
Jeremiah 1:4: Then the word of the LORD came unto me, saying,
Contradiction with Amos 3:7
Suggests that God reveals secrets to prophets, implying a different manner of communication than the straightforward proclamation in Luke 3:2.
Amos 3:7: Surely the Lord GOD will do nothing, but he revealeth his secret unto his servants the prophets.
Contradiction with Hebrews 1:1
Indicates that God spoke in diverse manners in past times, which may contrast with the singular event in Luke 3:2.
Hebrews 1:1: God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets,
Contradiction with 1 Samuel 3:1
States that the word of the Lord was rare in those days, which contrasts with the revelatory period of Luke 3:2.
1 Samuel 3:1: And the child Samuel ministered unto the LORD before Eli. And the word of the LORD was precious in those days; [there was] no open vision.