Captain Fleery is "a bony woman with pale eyes and hair the color of dust" (2.36). She uses her long limbs to point out the directions the messengers should go in, and she makes sure to give Lina thorough instructions on her first day on the job.
When Lina finds the mysterious message, she decides to ask Captain Fleery for help in looking at it, since "She would now about things like official documents" (7.10). Unfortunately, Captain Fleery is not much help because she assumes that it's a very old recipe or homework—nothing that's actually important.
What's more, as Lina and Captain Fleery talk about this message that's got Lina all worked up, Captain Fleery confides in Lina that she knows the Builders will return to save them all: "I have seen it in a dream. So have all of us, all the Believers" (7.36). Then she invites Lina to attend one of their meetings. We hope they're not serving Kool-Aid.