In this work, we study the Kähler-Ricci flow on rational homogeneous varieties exploring the interplay between projective algebraic geometry and representation theory which underlies the classical Borel-Weil theorem. By using elements of representation theory of semisimple Lie groups and Lie algebras, we give an explicit description for all solutions of the Kähler-Ricci flow with homogeneous initial condition. This description enables us to compute explicitly the maximal existence time for any solution starting at a homogeneous Kähler metric and obtain explicit upper and lower bounds for several geometric quantities along the flow, including curvatures, volume, diameter, and the first non-zero eigenvalue of the Laplacian. As an application of our main result, we investigate the relationship between certain numerical invariants associated with ample divisors and numerical invariants arising from solutions of the Kähler-Ricci flow in the homogeneous setting.