  In this paper, we discuss lumps (sigma model instantons) in flag manifold
sigma models. In particular, we focus on the moduli space of BPS lumps in
general K\"ahler flag manifold sigma models. Such a K\"ahler flag manifold,
which takes the form $\frac{U(n_1+\cdots+ n_{L+1})}{U(n_1) \times \cdots \times
U(n_{L+1})}$, can be realized as a vacuum moduli space of a $U(N_1) \times
\cdots \times U(N_L)$ quiver gauged linear sigma model. When the gauge coupling
constants are finite, the gauged linear sigma model admits BPS vortex
configurations, which reduce to BPS lumps in the low energy effective sigma
model in the large gauge coupling limit. We derive an ADHM-like quotient
construction of the moduli space of BPS vortices and lumps by generalizing the
quotient construction in $U(N)$ gauge theories by Hanany and Tong. As an
application, we check the dualities of the 2d models by computing the vortex
partition functions using the quotient construction.
