A fun day during the festival is the annual Blossom Kite Festival. This year it's scheduled for April 2, 2016 from 10 a.m. to 4:30 p.m. The event is free to attend and/or participate - fun for all ages. Throughout the day they'll be kite making, competitions, displays, challenges, battles and awards. For a more complete list of the day's kite events, see the full schedule (rain date is April 3). The fun all takes place at the Washington Monument.
While the National Cherry Blossom Festival has been running for years, this is the 6th year for the kite festival. I've never participated in the kite festival, but have wandered in to watch in previous years. It looks like a great time. Participants can bring their own kites or make one at an activity station (while supplies last).
In terms of the cherry blossoms, I was downtown about a week ago but there was nothing yet visible far as I could tell.
However, based on the signs of spring we're seeing here to the east of the District in Fairfax, I suspect the chances are good we'll see peak blossoms during the festival this year.
(A quick check to NPS's bloom watch page just confirmed it - I've been checking it frequently over the past few weeks. NPS is predicting the peak to be between March 31 and April 3 - perfect timing to see both the kites and the blossoms!)