<p>Motzkin paths represent many mathematical objects from different contexts with combinatorial flavor. In this paper, we exhibit an unexpected appearance of this family of paths in the network coding setting through a particular case of multishot codes called flag codes. A flag code is a set of flags, i.e., sequences of nested subspaces of a vector space over a finite field, with prescribed increasing dimensions. The flag distance is defined as the sum of the respective subspace distances and can be obtained in different ways, which considerably complicates the manipulation of these codes. Throughout this work we define the set of Motzkin paths associated with a flag code. This new invariant allows us to characterize some important families of flag codes and to extract relevant information about them. In particular, it gives us a direct way to compute the maximum possible number of combinations behind a prescribed value of the minimum distance.</p>