We live in a panopticon society, one where all our actions are continuously recorded, logged, and analyzed. I wonder, though, how these flights augment the FBI's investigations or operations. Why are they secret? Why are the planes registered under the name of front companies? Doesn't the FBI have all the information they need from the NSA or whoever else? I guess not. These flights clearly violate the fourth amendment, but whatever technology they are employing must be especially sensitive to justify the secretiveness of the program.
My best guess is they are creating a data set that includes complex imagery, perhaps using infrared or some similarly intrusive technology, and bulk collection of telecommunications signals. The end result might be a matrix-like understanding of the subject people, their movements, their communication patterns, and ultimately, how to manipulate scenarios for desired outcomes.
Plane registration N510KS, from July 21, 2015:
From July 22, 2015: