  The Euclid satellite, to be launched by ESA in 2022, will be a major
instrument for cosmology for the next decades. \Euclid\ is composed of two
instruments: the Visible (VIS) instrument and the Near Infrared Spectromete and
Photometer (NISP). In this work we estimate the implications of correlated
readout noise in the NISP detectors for the final in-flight flux measurements.
Considering the multiple accumulated (MACC) readout mode, for which the UTR (Up
The Ramp) exposure frames are averaged in groups, we derive an analytical
expression for the noise covariance matrix between groups in the presence of
correlated noise. We also characterize the correlated readout noise properties
in the NISP engineering grade detectors using long dark integrations. For this
purpose, we assume a $(1/f)^{\, \alpha}$-like noise model and fit the model
parameters to the data, obtaining typical values of $\sigma =
19.7^{+1.1}_{-0.8}$ e$^{-} \rm{Hz}^{-0.5}$, $f_{\rm{knee}} =
(5.2^{+1.8}_{-1.3}) \times 10^{-3} \, \rm{Hz}$ and $\alpha = 1.24
^{+0.26}_{-0.21}$. Furthermore, via realistic simulations and using a maximum
likelihood flux estimator we derive the bias between the input flux and the
recovered one. We find that using our analytical expression for the covariance
matrix of the correlated readout noise we diminish this bias by up to a factor
of four with respect to the white noise approximation for the covariance
matrix. Finally, we conclude that the final bias on the in-flight NISP flux
measurements should still be negligible even in the white noise approximation,
which is taken as a baseline for the Euclid\on-board processing
