Best way to calculate how fluids alter friction coefficients on an inclined plane

Have you studied much fluid dynamics? The issue with slowly flowing fluids isn't due to friction against the solid boundary (we usually assume there is infinite friction and that the fluid doesn't slip at all), it is all about the fluid's viscosity, which is basically a measure of its ability to slip over itself.

This can be measured with a viscometer.

 

Ah, I didn't realise it was for lubrication. I'm not sure to be honest, there is probably some good literature out there which describes standard testing for oils. But what you suggested makes sense, as long as you can ensure the volume of oils and particulars of the apparatus are kept constant, it sounds like a reasonable test.

Perhaps you might also try to keep the incline constant and drag the upper plate with a rope/pulley/weight combination, then measure the terminal velocity? That would give you a dynamic friction measurement, rather than a static friction measurement (which I think might depend very sensitively on the initial conditions and not be particularly relevant for lubrication, which is mostly concerned with moving parts).

I'm certain viscosity will be directly related to any results, but your approach seems far more practical.

 

The "standard" model is the Reynolds lubrication equation. http://www2.imperial.ac.uk/~ajm8/M3A10/lub.pdf (or google for other references).

But you will need to learn quite a bit of fluid dynamics, and math, before it makes much sense.