We present a MUSE and KMOS dynamical study 405 star-forming galaxies at redshift z=0.28-1.65 (median redshift z=0.84). Our sample are representative of star-forming, main-sequence galaxies, with star-formation rates of SFR=0.1-30Mo/yr and stellar masses M=10^8-10^11Mo. For 49+/-4% of our sample, the dynamics suggest rotational support, 24+/-3% are unresolved systems and 5+/-2% appear to be early-stage major mergers with components on 8-30kpc scales. The remaining 22+/-5% appear to be dynamically complex, irregular (or face-on systems). For galaxies whose dynamics suggest rotational support, we derive inclination corrected rotational velocities and show these systems lie on a similar scaling between stellar mass and specific angular momentum as local spirals with j*=J/M*\propto M^(2/3) but with a redshift evolution that scales as j*\propto M^{2/3}(1+z)^(-1). We identify a correlation between specific angular momentum and disk stability such that galaxies with the highest specific angular momentum, log(j*/M^(2/3))>2.5, are the most stable, with Toomre Q=1.10+/-0.18, compared to Q=0.53+/-0.22 for galaxies with log(j*/M^(2/3))