The extinction coefficient is measured by weighing out a specific amount of the dry chemical, dissolving it in a specific amount of the desired solvent to create a solution of a specific concentration, and measuring the absorbance spectrum of the solution using a spectrophotometer and a cuvette of a known path length. For dyes, which have strong absorbance, a rather dilute solution will be needed, such as 10 µM. This will require diluting the original stock solution. This dilution factor must be taken into account. Use Beer's law to calculate the extinction coefficient at the chosen wavelength from the measured absorbance, the known concentration, and the known pathlength:

Extinction coefficient = absorbance/(pathlength x concentration)

You can calculate this by using Beers Lamberts law from the absorbency measurement using UV Spectroscopy. 

I remember looking up the spectral data on this dye some time ago. This is what I found: For the AB dye solution, the concentration was determined via the absorption at λmax 566 nm (molar extinction coefficient was 16484.3 mol−1 cm−1) in the UV–vis spectra by using Shimadzu spectrophotometer UV-2600 (Japan) ( Lučić et al., 2014 and Pandiyarajan et al., 2015; Preethi, Anumary, Ashokkumar, & Thanikaivelan, 2013). I would use this as a first estimate and check the value on your sample as dyes may be slightly impure depending on the source.

Kind regards, Leo