Well I think Dash is very proud of superspeed. He gets really excited to use it whenever he can. Like when Elastigirl told him “I want you to run as fast as you can” you can tell he loves being told this. He is competitive and full of energy so, as said before, superspeed suits him.
I don’t think he’d be jealous of Violet’s powers themselves, but I think he might get jealous of the fact that she has two of them.
Being a young, competitive boy, I think he would appreciate the powers he has. I don’t think there’s any jealousy. I think the only thing Dash would be jealous about is never being put in charge of anything.
The superpowers that each of the family members has in the film are designed to fit their characters perfectly. Mr Incredible feels the need to be strong and protect his family (as a father) and others (as a super) whereas Elastigirl almost represents the mother who has to do everything and needs to “stretch” a little to make sure things fall into place. Violet is a shy teenage girl who’s only just realising her full potential, Dash is slightly hyper and competitive like many young boys, and Jack Jack is a baby who’s constantly changing with so many possibilities as to what he can become. These obviously aren’t just coincidences yet the characters have been developed well enough so that you realise their powers don’t JUST fit their current state and “stereotype”, but also fit their personality. I don’t think Dash is, or would become, jealous of Violet because he enjoys his power and it suits him well.