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We present VLT-SINFONI K-band integral field spectroscopy of the central galaxies in the cool core clusters A1664, A2204 and PKS 0745−191, to probe the spatio-kinematic properties of the Paα and ro-vibrational H2 line emission. In A1664, the two emission-line velocity systems seen in our previous Hα spectroscopy appear in both Paα and H2 emission, with notable morphological differences. The recession velocity of the red component of Paα increases linearly with decreasing radius, particularly along an 8 kpc filament aligned with the major axis of the underlying galaxy and the cluster X-ray emission. These kinematics are modelled as gravitational free-fall as gas cools rapidly out of the hot phase. In A2204, the gas shows three or four filaments reaching radii of 10 kpc, three of which lie towards ‘ghost bubbles’ seen in X-ray imaging by Sanders et al. For PKS 0745−191, we confirm the twin-arm morphology in the narrow-band images of Donahue et al.; the Paα kinematics suggest rotational motion about an axis aligned with the kiloparsec-scale radio jet; on nucleus, we find an underlying broad Paα component [full width at half-maximum (FWHM) ] and a secondary H2 velocity system redshifted by . The S(3)/Paα ratio is the highest in the most isolated and extended regions where it matches the levels in the NGC 1275 filaments as modelled by Ferland et al. Regions with much lower ratios highlight active star formation and are often kinematically quiescent (FWHM ). Our findings suggest that the three clusters may be captured in different stages of the ‘cold feedback’ cycle of Pizzolato & Soker, with A1664 in a short-lived phase of extreme cooling and star formation prior to an active galactic nucleus (AGN) heating event; PKS 0745−191 in an outburst state with the AGN accreting from a cool gas disc, and A2204 in a later phase in which cool gas is dragged out of the galaxy by the buoyant rise of old radio bubbles. [ABSTRACT FROM AUTHOR]