Chronic cough in children associated with flonase allergy?

Doubtful: I don't think a child would be allergic to the nasal steroid spray flonase. There are certainly children whose cough may not respond to treatment with flonase, but the reason is most likely a mis-diagnosis rather than an allergy to it. One needs to think about an infectious cause, asthma or possibly reflux to name a few reasons for lack of response to flonase.