In Chapter 23 of To Kill a Mockingbird, Scout decides that she wants to invite Walter Cunningham over for dinner and a sleepover once school resumes. Aunt Alexandra then retorts that the Cunninghams are "good folks... [b]ut they're not our kind of folks." She goes on to explain that Walter will never be like Jem and that the "drinking streak in that family is a mile wide." Although Aunt Alexandra wants Scout to be nice to Walter, she is not interested in allowing her to invite him home. Her final scathing remark on the Cunninghams is that they are "trash." 

Thus, the quote you're searching for arrives at the end of the chapter, when Jem and Scout discuss Jem's theory of the "four kinds of folks in the world": "the ordinary kind," "the kind like the Cunninghams out in the woods," "the kind like the Ewells down at the dump," and "the Negroes." You've slightly misremembered what Jem actually says in regards to this social order, although the meaning remains the same in the exact quote:

"...our kind of folks don't like the Cunninghams, the Cunninghams don't like the Ewells, and the Ewells hate and despise the colored folks." 

The page number will vary based upon the edition that you're reading; regardless, Jem is trying to suggest that there is always one "type" of people looking down on another. As you have mentioned, the Cunninghams have not accepted help from anyone, and, thus, choose to look down on the Ewells, who have relied on relief checks.

This comparison with the Cunninghams and Ewells comes during Jem's talk with Scout about his ideas of the social order in Maycomb (near the end of Chapter 23). According to Jem, there are four classes of people in town. There are (in descending order) the regular people, like the Finches; the rural country folks, like the Cunninghams; the Ewells; and the Negroes. Even Atticus, who rarely says a bad word about anyone, has labeled the Ewells "trash" and a "disgrace." Aunt Alexandra lumps the Cunninghams and Ewells together, believing that Walter Cunningham Jr. is not proper company for Scout--

"Because--he--is--trash, that's why you can't play with him."

--but Scout disagrees, telling Jem that

"... that boy's not trash, Jem. He ain't like the Ewells."