We study a simplified model of top-flavoured dark matter in the framework of Dark Minimal Flavour Violation. In this setup the coupling of the dark matter flavour triplet to right-handed up-type quarks constitutes the only new source of flavour and CP violation. The parameter space of the model is restricted by LHC searches with missing energy final states, by neutral D meson mixing data, by the observed dark matter relic abundance, and by the absence of signal in direct detection experiments. We consider all of these constraints in turn, studying their implications for the allowed parameter space. Imposing the mass limits and coupling benchmarks from collider searches, we then conduct a combined analysis of all the other constraints, revealing their non-trivial interplay. Especially interesting is the combination of direct detection and relic abundance constraints, having a severe impact on the structure of the dark matter coupling matrix. We point out that future bounds from upcoming direct detection experiments, such as XENON1T, XENONnT, LUX-ZEPLIN, and DARWIN, will exclude a large part of the parameter space and push the DM mass to higher values.