Artifacts are abilities only one player can have. When you take the Flag, you take it from whoever had it, if someone had it. So, they go back and forth. They're like Lost in the Woods (from Nocturne); hey could I do more with that kind of thing, I thought, and I could. There are five Artifacts total, and here are three of them and their parent cards.
Flag Bearer comes with a Flag. If someone takes it away from you, just buy another one. How many Flag Bearers can your deck tolerate, anyway? Well you can also trash them to get the Flag, so that won't always be an issue.
Swashbuckler is trickier. All that stuff after the colon only happens if you have cards in your discard pile - which is harder than it sounds. Part of it is, you draw the three cards before checking. The Coffers tokens don't have to have come from Swashbuckler specifically, so sometimes that helps, but you still need a discard pile at least once to get the Treasure Chest.
Treasurer can put you down a Treasure, up a Treasure, or even on Treasures. And the Key is like a Treasury. So it's sure to be a card you treasure.