Lost from Atlantis: Book 1

14 year old Katie Sullivan has vanished from modern day Atlanta and appears in 1197 A.D. Europe. Captured and taken as slave Katie makes a desperate wager with the king: If she can teach him how to fly, she won't only go free - she'll be rich! But if she fails she will die.
As a valued but distrusted advisor she counsels the monarchy on famine, bandits raiding the villages, emergency first aid, Black Plague, saves a woman from burning at the stake, and much more.
Could you convince a king in 1197 A.D. that you're worth more as an advisor than as a slave?