I'd google "Washington DC Events National Mall" and look for any planned events during your visit, especially if it's a weekend. Larger rallies, marathons, parades and such can really snarl weekend traffic, especially if they shut down Memorial Bridge which is one of the major arteries between DC and VA.

If no major events planned, and if traveling by taxi, I personally would leave the White House area around 2 to catch a 3:30 flight (boards at 3:00). This may be a little less time than others are comfortable with, but having flown out of DCA more times than I can count, it's pretty rare that you can't get from downtown to the airport, through security and to the gate in an hour. That's even if you are checking bags.

I would use the kiosks to print my BP as DCA still has not perfected the art of the mobile BP, seems to be a flaky equipment thing rather than a training thing, and it's not consistent, but it does seem to bite me whenever I am running short on time.