We are interested in triangulations of flat tori. A Delaunay flip algorithm performs Delaunay flips on the edges of an input triangulation T until it reaches a Delaunay triangulation. We prove that no sequence of Delaunay flips is longer than C_Γ • n^2 • Λ(T) where Λ(T) is the maximum length of an edge of T , n is the number of vertices of T , and C_Γ > 0 depends only on the flat torus. The bound improves on the preexisting upper bound in three ways: the dependency in the "quality" of the input triangulation is linear instead of quadratic, the bound is tight, and the "quality parameter" is simpler.