Saudi Arabian girl flying in Spain?

When you're in Spain, their laws apply to you. Since it is legal to fly anywhere without a male guardian, you can fly. But you still need a Visa to go to the states.

she would need to get the US visa when departing Saudi

You need a visa to travel to US (or elsewhere). You must prove you have sufficient funds of your own for all typical tourist expenses (round-trip tickets returning to your country of citizenship, hotels, restaurant meals, sightseeing, etc.). And you must prove your ties to your own country compel you to return to Saudi Arabia promptly, e.g. a lucrative job which affords you the luxury of expensive vacations. Highly unlikely you meet requirements for any tourist visa anywhere, especially when you are applying from a country other than your country of citizenship.

BTW, you are highly likely to be rejected for visa fraud, suspicions of intent to remain, or potential asylum fraud. You are NOT eligible for asylum anywhere in the world. Escaping your father's control is never grounds for asylum. And coming from a "safe" country also disqualifies you. You must apply at the nearest safe border when you are fleeing imminent danger of government persecution due to your political beliefs & actions, religion, etc.

As long as you are muslim, you attest to your acceptance of Sharia law & the tenets of your faith. And if you renounced islam, you would never be safe in any country which has any amount of muslim population, which eliminates any prospects of you being safe anywhere in Europe, North America, etc.

It's not that simple, you need a Visa to travel to the US, so even if she escaped from her family she wouldn't be able to travel to the US, even if she stays in Spain she would be returned to her country eventually

No, you would require a visa or you will not be getting on the flight

She would need a visa, which she will not be able to get, due to being a young person with no ties to her country, and no reason to return there.

yes, she could. Spain does not have the same laws as Saudi Arabia