You'll have to meet up with a character named Arzagos in Battania to learn the location of the second piece, and an imperial spy named Istiana for the last one.
You should already have the first one from completing the tutorial mission. Next, you'll be prompted to seek out two missing pieces of the Dragon Banner.Horses will allow you to get around faster and outrun any dangerous bandits who might want to pick a fight. During this phase, it might be better to keep a small army of mostly mounted troops so you don't need to worry about running out of money.They will suggest someone and give you their last known location. If you're having trouble, you can talk to any noble you run across (even one you've already talked to for this quest) and ask them who might be able to tell you more about the battle. The nobles who can fulfill this objective are scattered across the realm, so you'll have to travel far and wide to find them. First, you'll need to progress the main story quest by speaking to 10 different nobles about the Battle of Pendraic.