It is an interesting idea to think about Squeaky, in Toni Cade Bambara's "Raymond's Run," having much of any conflict because she is so self-confident and strong. She does have several, however. 

She is in conflict with her peers for several reasons because she does not think like most of them do. First, she does not see her mentally challenged brother as something to be made fun of like at least some of her classmates (and other people in town) do. He is her brother and she is determined to protect him from the dangers of just walking down the street as well as from unkind people.

Second, she thinks differently than others about things. While others are not too interested in working hard to achieve their goals, Squeaky works hard and does not mind that everyone else knows it.

Now some people like to act like things come easy to them, won’t let on that they practice. Not me. I’ll high-prance down 34th Street like a rodeo pony to keep my knees strong....

While others enjoy dressing up and showing off their finest clothing (which Squeaky sees as a waste of good money) or prancing around in a ridiculous costume, Squeaky is more concerned about being a decent human being. The last line of the story is a good reminder that too many of the girls she knows are

too busy being flowers or fairies or strawberries instead of something honest and worthy of respect . . . you know . . . like being people.

Squeaky is in direct conflict with Gretchen because they both intend to win the race. Squeaky says Gretchen  

has put out the tale that she is going to win the first-place medal this year. Ridiculous.

One conflict which is both internal and external is with Mr. Pearson. He intends to write her name down on his clipboard just as he knows her (which is not an outrageous thing for him to do); however, Squeaky chooses this moment to demonstrate her independence, as well as her individuality and personhood, by insisting he write down her full name: 

“Hazel Elizabeth Deborah Parker,” I correct him and tell him to write it down on his board. 

Squeaky also has a bit of an internal conflict when she decides that she could trade running, the thing that has been all-consuming for her, for training Raymond to run; however, it is rather an easy thing for her to decide. She may not do it, but she is willing.

In short, Squeaky knows what is important to her and is not afraid to show it. This attribute often puts her in conflict with others, but it is the kind of conflict she embraces.