  We present the power spectrum of galaxy clusters measured from the new
ROSAT-ESO Flux-Limited X-Ray (REFLEX II) galaxy cluster catalogue. This new
sample extends the flux limit of the original REFLEX to $1.8 \times 10^{-12}
erg/ s/cm^{2}$, yielding a total of 911 clusters with $\geq 94$ per cent
completeness in redshift follow-up. The analysis of the data is improved by
creating a set of 100 REFLEX II-like mock galaxy cluster catalogues built from
a suite of large volume LCDM N-body simulations (L-BASICC II). The measured
power spectrum is in agreement with the predictions from a LCDM cosmological
model. The measurements show the expected increase in the amplitude of the
power spectrum with increasing X-ray luminosity. On large scales, we show that
the shape of the measured power spectrum is compatible with a scale independent
bias and provide a model for the amplitude that allows us to connect our
measurements with a cosmological model. By implementing a luminosity-dependent
power spectrum estimator, we observe that the power spectrum measured from the
REFLEX II sample is weakly affected by flux-selection effects. The shape of the
measured power spectrum is compatible with a featureless power spectrum on
scales $k>0.01\,h/Mpc$ and hence no statistically significant signal of
baryonic acoustic oscillations can be detected. We show that the measured
REFLEX II power spectrum displays signatures of non-linear evolution.
