The outflows from neutrino-cooled black-hole (BH) accretion disks formed in neutron-star mergers or cores of collapsing stars are expected to be neutron-rich enough to explain a large fraction of elements created by the rapid neutron-capture (r-) process, but their precise chemical composition remains elusive. Here, we investigate the role of fast neutrino flavor conversion, motivated by the findings of our post-processing analysis that shows evidence of electron-neutrino lepton-number (ELN) crossings deep inside the disk, hence suggesting possibly non-trivial effects due to neutrino flavor mixing. We implement a parametric, dynamically self-consistent treatment of fast conversion in time-dependent simulations and examine the impact on the disk and its outflows. By activating the, otherwise inefficient, emission of heavy-lepton neutrinos, fast conversions enhance the disk cooling rates and reduce the absorption rates of electron-type neutrinos, causing a reduction of the electron fraction in the disk by 0.03 − 0.06 and in the ejected material by 0.01 − 0.03. The r-process yields are enhanced by typically no more than a factor of two, rendering the overall impact of fast conversions modest. The kilonova is prolonged as a net result of increased lanthanide opacities and enhanced radioactive heating rates. We observe only mild sensitivity to the disk mass, the condition for the onset of flavor conversion, and to the considered cases of flavor mixing. Remarkably, parametric models of flavor mixing that conserve the lepton numbers per family result in an overall smaller impact than models invoking three-flavor equipartition, often assumed in previous works.