Can we give her cyclobenzaprine 5 mg to reduce extreme anxiety when flying?

Incomplete question : It's best to discuss any medications with her doctor before giving them yourself. There are many things to consider, such as drug reaction, dosing size/strength, and drug safety, to name a few. There may be other options for her, and her doctor should be aware of this issue beforehand. You would not want to deal with an adverse drug reaction mid-flight.

Would not: That’s not a commonly recognized use for cyclobenzaprine, nor is it something with significant evidence to support its use. If the reason you are asking is because you notice that the drug - a muscle relaxant - causes drowsiness and fatigue - then absolutely not. Those are side effects and should not be reasons to dose the medication in someone for whom it was not prescribed.

No: Even a pathologist knows that a muscle-relaxant is a poor choice in treating situational anxiety. The best thing for fear-of-flying is preparation, learning about airplanes, and a friend to accompany you -- after talking about the purpose of the flight (to see those you love, to accomplish personal goals, or as it may be.) I'll let others recommend a benzodiazepine. Blue skies.