  Resolved rotation curves (RCs) are the gold-standard measurements for
inferring dark matter distributions in $\Lambda$CDM and testing alternative
theories of dynamics in galaxies. However they are expensive to obtain, making
them prohibitive for large galaxy samples and at higher redshift. Spatially
integrated HI flux profiles are more accessible and present the information in
a different form, but -- except in a highly compressed form, as linewidths --
have not so far been compared in detail with RCs or employed for dynamical
inferences. Here we study the consistency of RCs and HI surface density
profiles from SPARC with spatially integrated HI flux profiles from ALFALFA, by
combining the resolved properties in a forward model for the flux profile. We
define a new metric for asymmetry in the flux profiles, enabling us to cleanly
identify those unsuitable for our axisymmetric method. Among all SPARC galaxies
the agreement between RCs and flux profiles is satisfactory within the
limitations of the data -- with most galaxies having an uncertainty normalised
mean squared error (MSE) below 10 -- while no galaxy deemed symmetric has a MSE
above 1.2. Most cases of good agreement prefer a HI gas dispersion
$\sigma_{\mathrm{HI}}$ of ~13 km/s, consistent with resolved studies of gas
dispersion from the literature. These results open the door for spatially
integrated HI flux profiles to be used as proxies for spatially resolved
dynamics, including a robust appraisal of the degree of asymmetry.
