is there a way to determine a distant galaxy’s speed relative to the Hubble Flow by measuring time dilation effects between there and this galaxy?
No. Time dilation is expected and observed as a result of universal expansion (e.g. in the light curves of type Ia supernovae and the duration of gamma ray bursts, Blondin et al. 2008; Zhang et al. 2013). There is no way of distinguishing between a Doppler shift and cosmological redshift for an individual source.