I drove out to Joshua Tree the weekend before last to hunt up some flowers… and they were easy enough to find. The desert floor was blanketed with them as shown above.
Because of a long dry period these flowers might now be on their way out (the excellent DesertUSA flower report is showing that J-Tree’s peak flower time seems to be over). However, with some rain this week, the situation could very quickly change. Also, according to the report, the Antelope Valley Poppy Reserve is heavily in bloom right now.
I found that the best flowers, by far, are in the southern part of the park (shown below) by the 10 Freeway. This is the lower elevation part of the park in the Colorado desert. The high alititude Mojave desert zone, with all the fun-to-climb rocks, has very few flowers. The full map of the park is available here.