We stopped in DC last year to catch the Flames game during a road trip to the Smoky mountains last October. Traffic in and out was pretty bad (as is normal for that area). We used SpotHero for a parking reservation at an underground garage a few blocks from Capital One Arena. Had a great experience there, and the Flames winning in OT was the cherry on top
No issues wearing a Flames jersey there.
Can't speak too much for nearby attractions as we hit the road right after. But the arena looks close to many museums and attractions like the national mall and the different monuments.