There are no guarantees on what will bloom when. One advantage to Joshua Tree is that it has a variety of elevations, so perhaps one will be in bloom and those higher or lower will not. You may, however, have a difficult time finding a campsite in Joshua Tree NP; check the park's webpage for nearby alternatives.
Below is a fairly nice list, again no guarantees. The way things are looking today with the huge storm in Northern and Central CA , all of the flower seeds may wash away.
http://gocalifornia.about.com/od/topcalifornia/a/california-wildflowers.htmYou can get current reports when the time comes some of the links on that page. Always have plan B in mind.