I wouldn't change that much about her. The only thing I'd do is not give her a Dragonite outright, and instead give her a first-stage Dragon-type that would evolve over the course of the series. I think there's more value in starting with a weak Pokemon and working with it until it's strong than in taming an already strong Pokemon. The former shows the progression of the character over a long period of time with tangible moments of growth, while the latter occurs in a more condensed period of time and comes off as too sudden. Alternatively, I would have extended the Dragonite thing over more episodes and made the process of bonding and overcoming the boundaries between them more painful. During all of that, I would have emphasised the key flaw in Iris' character that prevents her from raising a strong Dragon-type in the first place, and only once she's overcome that would she be rewarded with the final stage evolution.
Besides all that, I wouldn't change anything about how she interacts with other characters. The contrast she has with Cilan is very strong while any problems with her relationship with Ash aren't a fault of her character, but a fault of how Ash is written in BW. Specifically, the issue liedwith Ash's lack of reactions to Iris' teasing/taunting. This had the unfortunate side effect of making Iris seem annoying through sheer repetition. While Ash's behaviour would give Iris more ammo to use against him, Ash himself was never interested in engaging Iris in that way and that killed the dynamic.