The normal dictionary expression for "taking wings unto itself" is "take to itself wings" meaning "your money disappears suddenly", but does it mean the same thing here? Did he go on bankrupt? He said to get along with Washington people, he needs money, that's why seems to be working in the West.
What is this "opening"?
Hearts and Hands by O. Henry
"My dear Miss Fairchild," said Easton, calmly, "I had to do something. Money has a way of taking wings unto itself, and you know it takes money to keep step with our crowd in Washington. I saw this opening in the West, and--well, a marshalship isn't quite as high a position as that of ambassador, but--"