With a very thick solution of ferric ammonium citrate and water, what
chemical can I add to it to make it dissolve at a very slow rate?

I'm not sure what you mean by a "thick" solution - could you describe
the problem in a bit more detail, please? Regardless, ferric ammonium
citrate is very soluble in water and will deliquesce, that is it will
pick up water from the air and dissolve in it. If you want to prevent
that you'll need to store it in an air-tight container. It's also
affected by light, so it needs to be kept in the dark, too. It's
almost insoluble in alcohols if that helps.

Ian G.

I inject this iron in trees and I am trying to control the release of
it inside the tree so it will release more slowly. I need a "chemical"
or whatever to add to the product so I can limit the rapid uptake in a
tree. The chemical can not be toxic to trees

I can't think of any direct way of making it dissolve more slowly. You
could try mixing it with something like gelatin or agar, but that's
nothing more than a guess. I've heard of people protecting seeds with
wallpaper paste, but I think they all contain fungicides and I don't
know what the long term effect would be on a tree.

Ian G.

Seems you want a 'slow release form' of FAC.  You might want to look
up semi-permeable membranes or other forms of slow release
formulations.  Can you pelletise your FAC, coat in some form of slowly
dissolving gum and then inject this emulsion into your trees?