By "bank slope", I assume you mean side slope. I don't think there is any calculation. Basically, I think you are limited to what you can install.
You should be able to install the mat at 1:1, I wouldn't go steeper.
8 fps is fine if the thickness is over 6". In PA, USA you can use Reno mats up to 18 fps, but watch shear stress = 62.4 x flow depth x bed slope. It must be 8.35 lb/sf or less, and at that flow rate, shear will probably limit design.
The other concern for reno mats are if your bank is too steep the rock begins to slump in the mat. This leads to increased tension on the wire mat. Do a google web search to find the company for reno mats. I recall seeing a table in some documentation, but it has been a few years since I have used one in design.
Another alternative to reno mats is 3x3xL gabions or just dumped/grouted riprap. Typically the mats are more expensive than grouting riprap.
I wouldn't go steeper than 2:1 with reno mattress. It is difficult construction on steeper slopes. You can anchor the mattress to the slope with a row of 3'x3' gabions at the top.
If you want steeper, construct a bank using stacked gabions. Stack them either at a slope or offset each layer to form steps. Maccaferri provides a wealth of design information and examples. Ask your local supplier for the literature.
I'm a little confused about the original question. If you know flowrate, then the velocity is a function of channel cross section and bed slope. Therefore, don't we know both the channel sideslopes and the bed slope already?
If the question is what are the slope limitations for reno mattress, are we talking about channel sideslope or bed slope? I think the channel sideslopes are not as much an issue as the channel bed slope. You're more likely to have problems with shear stress on the bed than on the sideslopes. I've used reno mattress and gabions a lot for landfill downchutes and was surprised recently when a manufacturer told me about the limiting bed slopes for these systems. I recall they were uncomfortable with even a 4H:1V bed slope. Companies like Maccaferri have good tech support and may be able to offer assistance.
One final thought- there are alternatives out there like fabric-formed concrete and concrete-filled geoweb.