In this paper, a multi-channel noise reduction algorithm is presented based on a Speech Distortion Weighted Multi-channel Wiener Filter (SDW-MWF) approach that incorporates a flexible weighting factor. A typical SDW-MWF uses a fixed weighting factor to trade-off between noise reduction and speech distortion without taking speech presence or speech absence into account. Consequently, the improvement in noise reduction comes at the cost of a higher speech distortion since the speech dominant segments and the noise dominant segments are weighted equally. Based on a two-state speech model with a noise-only and a speech+noise state, a solution is introduced that allows for a more flexible trade-off between noise reduction and speech distortion. Experimental results with hearing aid scenarios demonstrate that the proposed SDW-MWF incorporating the flexible weighting factor improves the signal-to-noise-ratio with lower speech distortion compared to a typical SDW-MWF and the SDW-MWF incorporating the conditional speech presence probability (SPP).