I'm not sure how well Access SQL supports SQL but at least with the ones I'm familiar with, using a subquery like that requires an alias. (It also needs to be it's own query- though again maybe Access does something weird that lets it understand "Brands INNER JOIN ..." as a subquery without a select clause?)
You should be able to use multiple Joins on the same query, so something like this might work:
select Products.Item, Products.UPC, Products.Price,Types.Type,Brands.BrandName
From Types
INNER JOIN Products ON Products.[TypeID]=Types.[TypeID]
INNER JOIN Brands ON Brands.[BrandID]=Products.[BrandID]