As part of our KMOS AGN Survey at High-redshift (KASHz), we present spatiallyresolved VLT/KMOS and VLT/SINFONI spectroscopic data and ALMA 870µm continuum imaging of eight z=1.4-2.6 moderate AGN (L 2−10kev = 10 42 −10 45 ergs s −1 ). We map [O iii], Hα and rest-frame FIR emission to search for any spatial anti-correlation between ionised outflows (traced by the [O iii] line) and star formation (SF; traced by Hα and FIR), that has previously been claimed for some high-z AGN and used as evidence for negative and/or positive AGN feedback. Firstly, we conclude that Hα is unreliable to map SF inside our AGN host galaxies based on: (i) SF rates inferred from attenuation-corrected Hα can lie below those inferred from FIR; (ii) the FIR continuum is more compact than the Hα emission by a factor of ∼ 2 on average; (iii) in half of our sample, we observe significant spatial offsets between the FIR and Hα emission, with an average offset of 1.4 ± 0.6 kpc. Secondly, for the five targets with outflows we find no evidence for a spatial anti-correlation between outflows and SF using either Hα or FIR as a tracer. This holds for our re-analysis of a famous z=1.6 X-ray AGN ('XID 2028') where positive and negative feedback has been previously claimed. Based on our results, any instantaneous impact on SF by ionised outflows must be subtle, either occurring on scales below our resolution, or on long timescales.