Welcome to Stamp Community Forum! The Cinderella area of collecting is so broad, and the percentage of cinderellas that have been documented and catalogued is so small, that you would be extremely lucky to find information on a particular item.
The best way to get a feel for value is to keep active in the market. If you scan
ebay's listing of cinderellas for several months, you will begin to get an idea of the kinds of material people are seeking, and what sellers are offering...topics, countries, eras, etc. Some areas are popular, and some are not, just like with postage stamps. You will probably see the same Cinderella offered for vastly different prices, and it will have nothing to do with condition. Some Cinderella sellers will never mention very bad condition problems with their material.
I search
ebay's Cinderella category regularly, and I don't remember having seen your item. Does that mean it is uncommon? Probably yes. Does that mean it is valuable? Maybe not, because if there are no or few collectors of Rhode Island labels, then there is no market, or a "thin" market.
If you keep searching (American Philatelic Research Library, microfilm of Rhode Island newspapers from 1936, etc.) you might find some information about your label. But, if you are looking for a listed value, I strongly suspect you will be disappointed.