  We construct covariant $q$-deformed holomorphic structures for all
finitely-generated relative Hopf modules over the irreducible quantum flag
manifolds endowed with their Heckenberger--Kolb calculi. In the classical limit
these reduce to modules of sections of holomorphic homogeneous vector bundles
over irreducible flag manifolds. For the case of simple relative Hopf modules,
we show that this covariant holomorphic structure is unique. This generalises
earlier work of Majid, Khalkhali, Landi, and van Suijlekom for line modules of
the Podle\'s sphere, and subsequent work of Khalkhali and Moatadelro for
general quantum projective space.
