I think the closest thing you'll find are those Amazon Sales Estimators from JungleScout & others. You can just pop that into a Google search and fill it out with the information such as which product category it's in and the seller's rank. Then you can get a close estimate of sales.
According to my clients it's pretty darn accurate.
To get the whole size of the market, I would find several of the top products and repeat this process. Then I'd assume that Amazon accounts for like 30-50% of total sales depending on the market. Hope this helps, good luck!