  We study the totally non-negative part of the complete flag variety and of
its tropicalization. We start by showing that Lusztig's notion of non-negative
complete flag variety coincides with the flags in the complete flag variety
which have non-negative Pl\"ucker coordinates. This mirrors the
characterization of the totally non-negative Grassmannian as those points in
the Grassmannian with all non-negative Pl\"ucker coordinates. We then study the
tropical complete flag variety and complete flag Dressian, which are two
tropical versions of the complete flag variety, capturing realizable and
abstract flags of tropical linear spaces, respectively. The complete flag
Dressian properly contains the tropical complete flag variety. However, we show
that the totally non-negative parts of these spaces coincide.
