Cold dark matter in the Milky Way halo may have structure defined by flows with low velocity dispersion .
The Axion Dark Matter eXperiment high resolution channel is especially sensitive to axions in such low velocity dispersion flows .
Results from a combined power spectra analysis of the high resolution channel axion search are presented along with a discussion of the assumptions underlying such an analysis .
We exclude KSVZ axion dark matter densities of \rho \gtrsim 0.2 GeV/cm ^ { 3 } and DFSZ densities of \rho \gtrsim 1.4 GeV/cm ^ { 3 } over a mass range of m _ { a } = 3.3 \mu eV to 3.69 \mu eV for models having velocity dispersions of \Delta \beta \lesssim 3 \times 10 ^ { -6 } .