  We derive the response of non-Hermitian topological phases with intrinsic
point gap topology to localized magnetic flux insertions. In two spatial
dimensions, we identify the necessary and sufficient conditions for a flux skin
effect that localizes an extensive number of in-gap modes at a flux core. In
three dimensions, we furthermore establish the existence of: a flux spectral
jump, where flux tube insertion fills up the entire point gap only at a single
parallel crystal momentum; a higher-order flux skin effect, which occurs at the
ends of flux tubes in presence of pseudo-inversion symmetry; and a flux
Majorana mode that represents a spectrally isolated mid-gap state in the
complex energy plane. We uniquely associate each non-Hermitian symmetry class
with intrinsic point gap topology with one of these cases or a trivial flux
response, and discuss possible experimental realizations.
