Could specific gravity be used to substitute viscosity?

I may be missing your point, but viscosity is the measurement of the resistance to flow of a liquid. If you don't have a viscometer, you can make a good substitute by getting some plastic (and metal, if needed) balls. Put your liquid to be measured into a tall graduated cylinger (which is transparent, such as glass) and drop various balls of different diameter and different mass into the liquid to be measured. Time the fall of the balls through a known distance thru the test liquids, and you can make a neat viscometer. In order to get any real information re the actual viscosity, you'd have to calibrate the "viscometer". Using such liquids as glycerine, polyethers of various known viscosities, various solvents etc for which accurate viscosities are published. The way one measures density of an unknown plastic is by using a very similar "viscometer" and various solvents. This is often the 1st step in identification of the plastic.

Specific gravity [SG] is the density of the material relative to the density of water, and is dimensionless: by definition, water has an SG of 1.0; most organic solvents are less and the interesting liquid metal Mercury [Hg] much more.

Viscosity is the relationship between the applied stress and the rate of strain. The MKS unit is the Newton-second-per-square-metre (Nsm^-2).

There is also the kinematic viscosity, which is the viscosity divided by the density, which has the units of m²s^-1, commonly referred to as Stokes, and usually manipulated in Centistokes.

Lyle's Golden Syrup, a familiar household substance (usual disclaimer - no connection other than as a satisfied customer) has a high viscosity and a low SG. Hg on the other hand has a low viscosity and a high SG.

It is not possible to infer one quantity from the other and all liquids of interest need to be assessed for their own individual characteristics.

Other posts have correctly explained the way to make a simple laboratory viscometer using ball bearings and tubes. Certain dimensions and characteristics becoming fixed produces a standard device, which can be used as a common reference - a rolling ball time viscometer. Common applications are to measure the viscosity of oils so as to indicate to the user their characteristics: "32 Second Heating Oil", "45 Second Gas Oil" being examples of the use of the terminology as common parlance. Clearly there is a relationship between the number of seconds of rolling ball time and the viscosity in Newton-seconds-per-square-metre or in Stokes, and this relationship is determined by calibrating the viscometer at a given temperature. The relationship is non-linear.

The viscosity of a fluid varies greatly with temperature; the SG rather less so.

Many fluids exhibit peculiar relationships between applied stress and rate of shear that make an instantaneous viscosity rather meaningless: tomato ketchup is a rheopectic pseudoplastic, for example, and an interesting video appeared on U-Tube recently of a fluid that could be walked over (without religious fervour!) and without falling into it, and yet would not support the weight of someone lying down in it.

Estimating properties by mixing known liquids together cannot accurately predict the viscosity and the density of the mix, as chemical reactions taking place in the mix will significantly alter the characterisitics. An example would be the mixing of epoxy resin and hardener in equal parts to produce a space-filling adhesive: "Araldite" (usual disclaimer) is an example in common parlance. The SG of the mix is about the same as the individual components, whereas the viscosity goes through the roof in a very short time...