The flow polytope associated to an acyclic graph is the set of all nonnegative flows on the edges of the graph with a fixed net flow at each vertex. I will discuss a family of subdivisions of certain flow polytopes and a polynomial invariant of these different subdivisions. I will give background on Schubert and Grothendieck polynomials, and then demonstrate how this polynomial invariant has a close connection to certain Schubert and Grothendieck polynomials. A consequence is that many interesting properties of the invariant carry over to Schubert polynomials in general, and Grothendieck polynomials conjecturally. I will finish with some questions about Schubert polynomials inspired by this research that remain mostly open.