Will the there be prophets in the times of Moshiach? Will everyone have some level of prophecy in the time of Mashiach? Or is prophecy gone forever?
A posuk in Yoel (3:1) seems to state that everyone will have prophesy in the time of Moshiach, which answers the question will prophesy return in the time of Moshiach:
היה אחרי כן אשפוך את רוחי על כל בשר, וניבאו בניכם ובנותיכים, זקניכם חלומות יחלמון, בחוריכם חזיונות יראו
And afterward I will pour out my spirit on all flesh , and your sons and daughters will be neviim, your elders will have dreams, your young men shall see visions.
The Rambam (Hilchos Teshuva 9:2:) writes that Moshaich will be a prophet:
[These changes will come about] because the king who will arise from David's descendants will be a greater master of knowledge than Solomon and a great prophet, close to the level of Moses, our teacher.
See also Melachim uMilchamot 12:3, where he writes that Moshaich will have "רוח הקודש".
At the time of mashiach, "knowledge of God will fill the earth as waters cover the ocean." (Chavakuk 2:14)
Whether or not this equals prophecy and future-telling is up for debate.