As part of our KMOS AGN Survey at High-redshift (KASHz), we present spatially-resolved VLT/KMOS and VLT/SINFONI spectroscopic data and ALMA 870$mu$m continuum imaging of eight $z$=1.4--2.6 moderate AGN ($L_{rm 2-10 rm kev}$ = $10^{42} - 10^{45}$ ergs s$^{-1}$). We map [OIII], H$alpha$ and rest-frame FIR emission to search for any spatial anti-correlation between ionised outflows (traced by the [OIII] line) and star formation (SF; traced by H$alpha$ 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 H$alpha$ is unreliable to map SF inside our AGN host galaxies based on: (i) SF rates inferred from attenuation-corrected H$alpha$ can lie below those inferred from FIR; (ii) the FIR continuum is more compact than the H$alpha$ emission by a factor of $sim 2$ on average; (iii) in half of our sample, we observe significant spatial offsets between the FIR and H$alpha$ emission, with an average offset of $1.4pm0.6$ kpc. Secondly, for the five targets with outflows we find no evidence for a spatial anti-correlation between outflows and SF using either H$alpha$ 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 impact on SF by ionised outflows must be subtle, either occurring on scales below our resolution, or on long timescales.
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