  Minimal Flavour Violation hypothesis can provide an attractive framework for
Dark Matter (DM). We consider scalar DM candidates carrying flavour quantum
numbers and whose representation under the flavour group guarantees DM
stability. They interact with the Standard Model fields through Higgs portal at
renormalisable level and also to quarks through dimension-6 operators. We
provide a systematic analysis of the viable parameter space for the DM fields,
which are triplet of the flavour group, considering several DM-quark
interactions. In this framework, we analyse in which cases the viable parameter
space differs from Higgs portal models thanks to the underlying flavour
structure. In contrast to minimal Higgs portal scenarios, we find that light DM
in the GeV mass range as well as heavier candidates above Higgs resonance could
be allowed by colliders, direct and indirect DM detection searches as well as
flavour constraints. The large mass regime above the top mass could even be
beyond the reach of future experiments such as Xenon 1T.
