Is the protagonist of The Spy flat or round? What purposes are served by the traits of flat or round characterization?

The answer is to this is that Isaac Bell is not developed as a round character. He is a flat character, but this is in keeping with conventions of the detective murder mystery genre, which puts the solution of the crime above other structural considerations. Having a flat character as the detective protagonist in a murder mystery serves the function of channeling focus onto the challenge of finding and understanding clues unlocking the mystery.
As a flat character, Bell is drawn as personable and sympathetic by the use of defining characteristics, but he remains at the end of the mystery story virtually as he is at the beginning: solving the mystery is his job, not an opportunity for life lessons and epiphanies (as would be the case for a round character).

"Would you mind if I waited?" Bell asked with a smile that flashed his even teeth and lighted his blue eyes.

Even though a flat character, we are given insight into Bell's moral and ethical character traits. For example, we see his ethical traits when he says that he doesn't want to "leave John Scully in a lurch" on the Frye Boys case, and we see his moral traits when he chooses to dig deeper into Dorothy Langner's request because she is "passionate" about her father's work and struck "oddly" by the handwriting in the suicide note.
In the detective murder mystery genre, a flat detective serves the purpose of structural development around solving the mystery, saving the good by-standers, saving the good reputation of the victim and bringing the perpetrator to justice. In serving the purpose of the plot in this way, it is not necessary for the detective to have personal development, to grow and change--to be a round character--while doing so.
The purpose of a round character, in contrast, is to bring the protagonist and the reader through an in-depth life experience, the result of which is change and growth ending in a deeper knowledge, appreciation and understanding of life, nature, others or self.   
https://www.britannica.com/art/flat-character