  We study flat bands and their topology in 2D materials with quadratic band
crossing points (QBCPs) under periodic strain. In contrast to Dirac points in
graphene, where strain acts as a vector potential, strain for QBCPs serves as a
director potential with angular momentum $\ell=2$. We prove that when the
strengths of the strain fields hit certain ``magic" values, exact flat bands
with $C=\pm 1$ emerge at charge neutrality point in the chiral limit, in strong
analogy to magic angle twisted bilayer graphene. These flat bands have ideal
quantum geometry for the realization of fractional Chern insulators, and they
are always fragile topological. The number of flat bands can be doubled for
certain point group, and the interacting Hamiltonian is exactly solvable at
integer fillings. We further demonstrate the stability of these flat bands
against deviations from the chiral limit, and discuss possible realization in
2D materials.
