I dont think there is a specific store for those kind of products, but there is a list provided by the BDS movement where you can check out the products that you could buy. But you could always go more local, like instead of buying coffee mate creamer, you could buy rainbow products which are more local.
You can find it @Cozmo they have a whole shelf filled with different brand and prices, you can also check out @Cashmere Cosmetics but I am not sure that they have it.
You might be able to find it at any supermarket in Amman that sells Heats, however if you don't you can always buy it from @Swefieh Village there is a shop there right next to @Majnoon Qahwa you will find the Teak selection there for sure.