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This work focuses on determining the fluence rate of a moderated ($\alpha$, n) neutron source, a key parameter required for assessing the activation levels in metal and concrete samples. Activation studies are an important tool for nuclear decommissioning. By activating material samples in controlled conditions in a known neutron fluence rate, the expected activity in decommissioning can be estimated. The fluence rate is determined by an absolute measurement of the accumulated activity of neutron-activated reference samples with a well known composition and a cross section using a $\beta\gamma$ coincidence setup. Accumulated activity determination requires both single $\beta$ - and $\gamma$ - detection, as well as coincidence data. A main advantage of this technique is that the resulting measurement is mostly independent of individual detector efficiencies. The current setup uses three detector combinations, consisting of three $\gamma$ (High Purity Germanium (HPGe), 2$\times$2 inch cylindrical cerium bromide (CeBr$_3$), and 3$\times$3 inch cylindrical sodium iodide (NaI) scintillators) and two $\beta$ detectors (a sample-enclosing and a 1 mm thick cylindrical plastic scintillators), paired with a multi-channel data acquisition system, separately recording hits in the $\beta$ - and $\gamma$ - channels including their timestamps. Coincidences are extracted in the offline analysis from the stored data. Having non- and coincident data in one dataset reduces the impact of certain corrections, e.g. dead time. Additionally, Monte Carlo techniques were implemented to assess $\gamma$ - interactions in the $\beta$ - detector and to account for finite energy resolution in $\gamma$ - detectors. Samples, including aluminum ($^{27}$Al), gold ($^{197}$Au), silver ($^{107}$Ag and $^{109}$Ag), Vanadium ($^{51}$V) and sodium chloride (NaCl) were activated. Calculated thermal fluence rates from different samples agree within uncertainties, with an average fluence rate of $(2.11\pm0.09)\times 10^5 \text{ cm}^{-2} \text{ s}^{-1}$ (uncertainty is given with a coverage factor of 2, that is the true value is within 95 % probability within this interval). Reaction products from (n, p) and (n, 2n) reactions induced by fast neutrons are also detected. Their fraction is, however, too low to be exploited quantitatively.