I'm having trouble finding examples of white privilege in children's literature
Thanks for your question!
I pulled out from a specific "white privilege" search and searched more broadly for "racism" and "civil rights" in children's literature, and found quite a few examples of white privilege:
The Mighty Miss Malone, about a the hardships of a poor black family in Flint Michigan during the depression. (This and pretty much anything by Christopher Paul Curtis will have some examples of privilege.)
The Yard War, by Taylor Kitchings. Twelve-year-old Trip Westbrook lives in Jackson, Mississippi, in 1964 and discovers the underlying racism in his family and neighborhood when he invites his maid's son Dee to play football in the yard.
The Lions of Little Rock, by Kristin Levine, is set in 1958 Little Rock, Arkansas, as it grapples with integration. One of the main characters is a black girl revealed to be "passing" as white.
Riding to Washington, by Gwenyth Swain, about a white girl's experience as she rides the bus to witness Martin Luther King's "I Have a Dream" speech.
This was just a quick search, and I noticed all of these fall during the civil rights era if not before. Please let me know if you need stories set in a more current period. I know they exist as well, just a bit harder to track down.
Thanks again for asking!