What kind of data do you have, stress relaxation, dynamic moduli etc?

As far as seen, we do not have a single coefficient to be defined as "viscoelastic coefficient". The only parameter of importance connecting all these parameters is the "viscoelastic relaxation phase velocity" dealing both with "memory-" and "dissipative-" effects. A generalized hydrodynamic description for estimating your varied coefficients of interest may be found at

Frenkel, J.: Kinetic Theory of Liquids. Clarendon, Oxford (1946)

Landau, L.D., Lifshitz, E.M.: Fluid Mechanics. Pergamon Press, Elmsford (1987)

https://www.sciencedirect.com/search?qs=viscoelastic%20coefficient%20of%20Kelvin-Voigt%20Model&show=25&sortBy=relevance

If you have experimental data and the Kelvin Voigh Model, you could use any optimization method (PSO least squares, gradient methods, etc.) to minimize the error (Ymodel -Yexp) so that both model and data can be adjusted

I think your question lacks a bit of context as the K-V model can be applied to a variety of situations, from actual spring-damper system in mechanical devices to fluids and solids under loads, and more. As you specified that it is for materials, you may want to specify which materials and conditions, or at least the material phase to get a detailed answer.

Nevertheless, I think that from a general standpoint, Mr. Hernández answer's is right. You usually curve fit the model to actual test data. However, the test will depend on the type of material and conditions.

You may want to search the web for ''basic elasticity and viscoelasticity princeton university press'' for a primer on materials mechanics and the relation of the K-V model to actual behaviour (although fitting is not really discussed).

Test standards as ''ASTM D6048—07 (Reapproved 2012) Standard Practice for Stress Relaxation Testing of Raw Rubber, Unvulcanized Rubber Compounds, and Thermoplastic Elastomers1'' may also help you.

Best regards,

Laurent

Here's a lovely recent paper on the topic

https://aip.scitation.org/doi/pdf/10.1063/1.4975417?class=pdf