Disclaimer: I do not own FMA.
Summary: My theory on why Edward liked to wear a red coat.
Edward Elric wore a red coat on that day he left his hometown with his younger brother Alphonse Elric. Nobody thought anything of it.
They met the Colonel Roy Mustang at the train station where the military took away terrorists that they had helped to catch. Alphonse learned that the Colonel's title was the Flame Alchemist. For the first time, he wondered why his brother wore red.
Then his brother got his own title and became known as the FullMetal Alchemist. Alphonse had thought that Edward will go and get a coat with more subdued colours. Instead he had continued to wear that red coat. Red makes him think of flames and fire.
His brother and the colonel argued non-stop. They even went as far as fighting each other as their yearly assessment which every State Alchemist has to go through. Once again, Alphonse wondered why Edward wore colours that reminded him of the Flame Alchemist if he hated the Colonel so much.
The night after he got his body back, Alphonse caught them kissing in the car. Finally his question was answered.