I understand that Kuba is vomiting and is refusing to eat despite an anti-nausea injection and had blood work which showed high blood calcium levels.
Slime is made up of Elmer's glue and liquid starch which are both water soluble glues, and sometimes Borax, which is a desiccant.
That means that once those glues hit her stomach they are very likely to be diluted out and dissolve. While they both may cause some irritation and nausea, they are not truly toxic.
Sodium tetraborate (Borax), is a fairly safe chemical. It is a desiccant, but a dog would have to eat huge quantities to even see stomach upset and that would be the only thing you are likely to see.
None of these things would cause elevations in his blood calcium.
I suspect that eating slime could contribute to his initial nausea and vomiting, but he should be better by now if it was just related to that. I suspect that there is something else going on.
High levels of vitamin D (cholecalciferol) found in rat poisons, a parathyroid tumor, lymphoma (cancer of the lymph nodes), anal sac gland tumors, multiple myeloma, bone tumors, hypoadrenocorticism, kidney disease (failure), and some types of fungal infections can all cause hypercalcemia.
It sounds like your veterinarian believes his symptoms are related to kidney failure if they prescribed a special diet.
If he is still vomiting though he should be hospitalized for intravenous fluids, anti-nausea injections, and something to coat his stomach.
Please let me know if you have any further questions.