@Walter_vi_Britannia He blushed because she caught him in a lie. He was simply embarrassed, especially since he was outed by a child while he's a grown adult. As she mentioned he seems to actually be a very straightforward person, and one potential way of interpreting this is he is pure of heart. This could also explain why he is unwilling to have mistresses as he likely desires a single wife he can dedicate himself to. Just so happens his current fiance is still but a child.
With that said, he could actually be quite different than what I've suggested. As we still know very little about the Crown Price, we won't know for sure what kind of person he actually is until later chapters provide us with more information.