  Anomalous symmetries are known to strongly constrain the possible IR behavior
along any renormalization group (RG) flow. Recently, the extension of the
notion of symmetry in QFT has provided new types of anomalies with a
corresponding new class of constraints on RG flows. In this paper, we derive
the constraints imposed on RG flows from anomalies that can only be activated
in the presence of specific background fluxes even though they do not
necessarily correspond to a symmetry. We show that such anomalies can only be
matched by gapped theories that exhibit either spontaneous symmetry breaking or
symmetry fractionalization. In addition, we exhibit previously unstudied
examples of these flux background anomalies that arise in $4d$ QCD and $4d$
SUSY QCD.
