sure you can paint over a silky fabric.
like i said - wet it down first and then let it dry because it will have some coating on it and the paint might not go on evenly.
FolkArt is the brand at Michael's with the most colours. for those lampshades try two 2 oz. bottles of colour and one bottle of Textile Medium. mix them up in a re-sealable container so you can add a thin layer until you get the right tone. let it dry completely between coats of paint.
a 1-inch synthetic brush will work and it will clean up with soap and water.
let me know if you decide to do it and how it works.