Explanation a flat fading channel in case MIMO OFDM
Frequency-flat fading essentially means that the channel's transfer function is (approximately) constant in your frequency band of interest, which means you can treat it as if it would not depend on frequency at all. This means two things:


Your MIMO transmission model is simply $\mathbf y(t) = \mathbf H \mathbf x(t) + \mathbf w(t)$ with a transmit signal $\mathbf x(t)$, a MIMO channel matrix $\mathbf H$, a received signal $\mathbf y(t)$ and your additive noise $\mathbf w(t)$. Note that $\mathbf x(t)$ needs to be narrow-band for this to make sense.
Your wouldn't use OFDM in this case. It just doesn't make sense: Every subcarrier would see exactly the same channel and you would gain nothing from the OFDM pre/post processing.


As for modelling the elements of your channel matrix, you can use statistical models that assume some random distribution that the elements are drawn from but be wary of the assumptions those are derived under. For instance, if you assume dense multipath from all directions, you end up with a Rayleigh distribution (resembling a case where you have rich scattering and no line of sight component). For cases with line of sight you might want to consider a Rician distribution. This is fine for not too high frequencies. For mmWave bands, this would be a bad model, since there the multipath is typically quite sparse and your channel matrix tends to be low rank.