We were there from the 5th through the 11th. You don't have to worry about getting a campsite. Sunset Campground at Furnace Creek is kind of an overflow area and more sections are opened as needed. We got there Saturday afternoon and there were still sites left. It's just a big parking lot.
We moved to Texas Springs the next day and stayed there for four days. Texas Springs is a no generator zone. It has picnic tables and fire rings. The sites are close together but fairly long.
Furnace Creek Campground is the only one that takes reservations so you could check for cancellations.
The flowers are still incredible. It's definitely worth the trip but be aware that the fall flooding has closed some of the roads.