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If the bird’s natural speed is 7mph, and the tail wind is 7mph, the bird is still flying at 7mph airspeed, its ground speed just increases to 14mph.

No different than a jet flying with or against the jet stream.

https://science.howstuffworks.com/transport/flight/modern/ai...

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that is my point - in order to stay up, the bird would need to either flap its wings for 700 miles non-stop (unlikely) in order to maintain velocity difference between it and the ambient air OR glide which basically means he was not traveling at the speed of ambient air, otherwise there would be no lift pressure generated on his wings and he would drop to the ground

Ignore the storm for a moment, and ask whether a bird can fly for 7h+, either from flapping, gliding, or navigating updrafts. The answer is yes, that's trivial for many many bird species, especially those with a propensity for ocean travel. The storm then just changes the baseline ground speed.

There's stuff like dynamic soaring that Albatrosses use to travel thousands of miles over the ocean using little energy.

Some enthusiasts use this to make RC gliders go really fast, and the record is over 500 mph.

https://en.wikipedia.org/wiki/Dynamic_soaring

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