For glutenfree cosmo has a good selection of products, as has Miles. Carrefour has a little, and also Spinney has a good diet section with glutenfree items Which one is the best depends on which brands you prefer, and also it can differ by the week (not all the products are always available). Prices are more or less the same everywhere and is glutenfree in general not cheap, in Jordan it is is even more expensive. I prefer Spinney.
Besides that there is a bakery in sweifiyye Al Sufara who has a large range of glutenfree products (rice bread, corn bread, cookies etc.) but it is a bakery where also normal stuff is prepared, so how about cross contamination, I am not sure (and I don't take the risk)
Glutenfree is quite unknown in Jordan, although sometimes in restaurants or cafe's "glutenfree" shows up, Amman@cafe has glutenfree pasta (but I don't know if they still have).
Not in every restaurant everybody speaks English very well, so if you also want to go out for dinner make sure you have a diet card explaining what Celiac is, also in Arabic and since restaurants don't have that much experience with glutenfree diet, it also can be useful to tell them what you can eat instead of only mentioning what you can't it.
I wish your friend a good (glutenfree) stay in Jordan.