I'm thinking of not buying my daughter a new jacket.
Why would you not give your daughter a jacket?
Because I think if I give her one, she will brag about it.
You are expected, as a parent, to provide for your child. You should buy her the jacket.
If it's going to make her proud, then I don't want her to get a jacket.
A jacket isn't anything flamboyant to be giving to your child. You should cherish the gifts you give to your kids and if they want to show it off, then tell them to stay humble about it.