Did Jesus ever ask the Father to make him into flesh so that He could come to earth and redeem us?
The Bible does not give us the answer to your question.
We are told, however, that Jesus came to this earth to die for us because He wanted to! In the book of Hebrews, we read that He came to do the will of God the Father. He willingly came here and died for us.
. . . then He said, “BEHOLD, I HAVE COME TO DO THY WILL.” . . . By this will we have been sanctified through the offering of the body of Jesus Christ once for all. And every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins; but He, having offered one sacrifice for sins for all time, SAT DOWN AT THE RIGHT HAND OF GOD, waiting from that time onward UNTIL HIS ENEMIES BE MADE A FOOTSTOOL FOR HIS FEET. (NASB) Heb. 10:9-13
When Jesus came, He took on human flesh. He was not ashamed to look like us either.
For both He who sanctifies and those who are sanctified are all from one Father; for which reason He is not ashamed to call them brethren . . . (NASB) Heb. 2:11
It is wonderful to realize that God was not ashamed to look like us. He was not ashamed of us. He may not like our sinful habits, but He does not reject us. He loves all of us, especially those who believe in Him – Christians.