Hi, welcome to the ehealth forum and I am glad to help you.
You seem to be concerned by the recurrent kidney stones and the composition of kidney stones.
There is nothing like kidney stones made of protein but a high protein diet has been postulated to increase the incidence of stones as protein from meat and other animal products is broken down into acids, including uric acid. The most available alkaline base to balance the acid from protein is calcium phosphate (hydroxyapatite) from the bones (buffering). Other types of stones in addition to the uric acid stones include the more common calcium stones. Calcium oxalate and calcium phosphate stones make up 75 to 85% of the total stones prevalent.Cystine and struvite stones complete the list of stone types.
Hope this helps. Take care.
Note: This post is not to emphasise final diagnosis as the same cannot be made online and is aimed just to provide medical information and no treatment suggested above be taken without face to face consultation with health care professional.