Jen - Have been there and done that with two. I can tell you quite honestly to go with your instincts of what is best for you and your child.
DD8, like your son, has a June birthday, so she was the youngest in her class. Per her report card, she had all the skills she needed to go from K to 1st. We discussed with her K teacher, more than once, about having her repeat Kindergarten. Per the teacher, she was just fine and more than ready.
So, we go to the 1st parent/teacher conference for 1st grade and the 1st thing she asks us, did we ever think of holding DD back, becasue she is behind on so many of the skills, especially reading. Needless to say, something hit the fan. Told her what we had discussed the the K teacher and what she told us. Per the 1st grade teacher, THEY the teachers can't suggest to a parent to have a child repeat, but if a parent is questioning it, they are to provide accurate info for the parents to make a decision. Our K teacher did not advise correctly, which, according to the 1st grade teacher, our DD wasn't the only one in her class from this K teacher, that really wasn't ready for 1st. We made the decision to leave her in 1st and she how she progressed. By the end of the year, her reading was still only at an early 1st grade level. We had her repeat 1st grade. The 2nd time around was a wold of difference. With her reading over the summer, she started the school year at an improved reading level and she made honor roll all year.
With our son, his wasn't so much he didn't learn, but a teacher just flat out not liking a student and not doing anything to teach this student. DS has ADHA and if you don't make lessons interesting, his attention goes down the drain. The teacher that he had for 3rd, had a hard and fast rule, the kids put their hands on their desks, hands in laps and their minds and ears on her voice. Becasue of his ADHA and speech impediment, he has a modified learning schedule. This teacher WOULD NOT, modify her assisgnments to meet his BY LAW ordered schedule. And yes, the principle and the school administration were made very well aware of her issues. There was another girl in this class, on a modified schedule and she was given assistance and the modification her order called for, but not my son. So by the end of the year, this teacher was ready to pass him onto the 4th grade. When I questions about his reading level, I was told that, that wasn't really important, as he had made grades good enough to pass to 4th. Needless to say, once I went to the principle and demaded to know what his level was, he was only at late 2nd/early 3rd grade level. He repeated 3rd grade last year, and what a difference a year and a different teacher makes. He was on the honor roll all of last year. And he enjoyed school.
Trust your judgement. If you really feel that having your DS repeat, do so.