  This paper is a direct generalization of Baker-Bowler theory to flag
matroids, including its moduli interpretation as developed by Baker and the
second author for matroids. More explicitly, we extend the notion of flag
matroids to flag matroids over any tract, provide cryptomorphic descriptions in
terms of basis axioms (Grassmann-Pl\"ucker functions), circuit/vector axioms
and dual pairs, including additional characterizations in the case of perfect
tracts. We establish duality of flag matroids and construct minors. Based on
the theory of ordered blue schemes, we introduce flag matroid bundles and
construct their moduli space, which leads to algebro-geometric descriptions of
duality and minors. Taking rational points recovers flag varieties in several
geometric contexts: over (topological) fields, in tropical geometry, and as a
generalization of the MacPhersonian.
