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The Kindle app on iOS gets blocked attempting to connect to Facebook every time I open it.

Blocked by what?

AdGuard Pro with facebook.com and facebook.net added to its DNS blacklist.

When the app attempts to connect to graph.facebook.com it gets NXDOMAIN.

You are wording this in a way that it implies that this (block) happens by ios. That's not true and you know it.

Did you not see the follow-up sibling comment clarifying this? (That was posted 2 hours before yours)

It should have been an edit to the original comment.