  Models incorporating flavoured dark matter provide an elegant solution to the
dark matter problem, evading the tight LHC and direct direction constraints on
simple WIMP models. In Dark Minimal Flavour Violation, a simple framework of
flavoured dark matter with new sources of flavour violation, the constraints
from thermal freeze-out, direct detection experiments, and flavour physics
create well-defined benchmark scenarios for these models. We study the LHC
phenomenology of four such scenarios, focusing on final states where a single
top quark is produced accompanied by no jets, one jet from the fragmentation of
light quarks or a $b$-tagged jet. For each of these signatures we develop a
realistic LHC analysis, and we show that the proposed analyses would increase
the parameter space coverage for the four benchmarks, compared to existing
flavour-conserving LHC analyses. Finally we show the projected discovery
potential of the considered signatures for the full LHC statistics at 14 TeV,
and for the High Luminosity LHC.
