An easy way to measure refractive index is to use Brewster angle technique. The angle at which minimum reflection(or zero for properly polarized light)observed is the Brewster angle and tan of the Brewster angle will give refractive index of the glass.
The easiest way to measure the index of a glass is the Becke line technique used by geologist and glass scientist. But you would need a set of index matching oils and a microscope. You can get and estimate by using the baseline offset from an optical spectra.
If you just want to calculate a very good estimate from the known composition, try the calculator in the SciGlass database. There are a number of published sets of values for the contributions from each oxide, which are multiplied by the fraction of that oxide in the glass. The total is an estimate of the index. If you have a really exotic composition (fluoride, e.g.) you can't use this method very well. As far as I know, the only fractional component values are for oxide glasses. Unfortunately, I don't remember the sources for any of those sets of values.
Sorry, I didn't know that SciGlass didn't work anymore. I retired several years ago and don't keep up with those things anymore.
There is also a book published by Schott glass which has a good set of factors for calculating the index of commercial type glasses. Don't remember the details and no longer have a copy of the book.