  Linear degenerate flag varieties are degenerations of flag varieties as
quiver Grassmannians. For type A flag varieties, we obtain characterizations of
flatness, irreducibility and normality of these degenerations via rank tuples.
Some of them are shown to be isomorphic to Schubert varieties and can be
realized as highest weight orbits of partially degenerate Lie algebras,
generalizing the corresponding results on degenerate flag varieties. To study
normality, cell decompositions of quiver Grassmannians are constructed in a
wider context of equioriented quivers of type A.
