The first source mentioning clouds as a mode of transportation of the Jewish people to the Land of Israel is the prophet Daniel (7:13): “I saw in the visions of the night, and behold with the clouds of the heaven, one like a man was coming, and he came up to the Ancient of Days and was brought before Him.” Rashi explains that this man is Moshiach (the Messiah) who judges the nations.
Another source is the Talmud (Sanhedrin 98a) where two scenarios for Moshiach’s appearance are cited: if the Jews are meritorious, he will arrive on a heavenly cloud, if not, he will come as a poor man riding a donkey.
In Yalkut Shimoni (Isaiah 503) it says that just like during the Exodus from Egypt, when the A-mighty led the Jewish people with the Clouds of Glory (Exodus 19:4) “You have seen what I did to the Egyptians, and [how] I bore you on eagles' wings, and I brought you to Me.”, He will likewise do so in the future (Isaiah 60:8) – “Who are these that fly like a cloud?” Understandably, the reference here is to all Jews.
In the Talmud (Baba Basra 75a) it says that in the future, G-d will raise Jerusalem to a height of approximately 10 miles, as it says (Zechariah 14:10): “But it [Jerusalem] will be elevated high and remain in its old place.”
When the Temple stood, the Jewish would go there three times a year. In Psikta Rabati it says that after the Redemption, this will occur much more frequently.
As the prophet says (Isaiah 66:23): “And it shall be from new moon to new moon and from Sabbath to Sabbath, that all flesh shall come to prostrate themselves before Me," says the Lord.”
The Lubavitcher Rebbe Shlita King Moshiach explains (Maamarim 5737, pp. 299-300) that even Moshiach’s coming on Shabbat would not be problematic from the standpoint of laws regarding traveling within the maximally allowable distance.