"fled embracing" is correct and can be used in written English
You can use it to indicate that two people were embracing each other as they fled, indicating either the intensity of their emotion or the tragedy of them having to leave each other. For example: "The two lovers fled embracing, never to see each other again."
Millennials may want to flee banks, but embracing every disruptive fintech offering simply because it doesn't come from a bank would be foolish and potentially as risky as taking out a subprime mortgage with no money down.
But what they do know is they have experienced great joy in a few short months as their children have fled failure and embraced not only positive academic outcomes, but in many cases environments that support students' self-esteem and reinforce their desire to learn.
But for much of history many feminists have come out on the side of fleeing from nature, not embracing it.
After converting his mother and brothers to his beliefs, he and the family fled to Amsterdam and embraced Judaism.
The orphaned daughter of German Jewish refugees who fled the Nazis and embraced all things American, Hester is obsessed by Herr Prof. Heinrich Falk, a German medievalist 20 years her senior.
The nation's first full-time graduate theological school, the Andover Theological Seminary was started by orthodox Calvinists who fled Harvard after it embraced Unitarianism.
Stocks were mixed again as investors fled technology issues and embraced defensive stocks.
Democrats flee what they should embrace, while Republicans embrace what they should flee.
His so-called "Muslim ban" remains in legal limbo but he has clearly indicated an aversion to embracing Syrian refugees fleeing from the horrors of war.
I should know: I myself have a degree in electrical engineering – but I fled to the warm embrace of software as soon as I graduated.
