I would be very carefully going down 'chicken and rice' road. I was in the same situation. Underweight puppy girl, who was 8 months and 35lb, having constant diarrhea.
Vet recommended chicken and rice for a week; it took me two months to get her eating a dog food again. At some point she went 3 days without eating, refusing a dog food! After that she would pick half of the cup a day to just get by. She was so skinny that having very little food in her stomach didn't bother her at all. When I tried to mix dry food with her favorite rice and chicken, she would just lick the chicken off, leaving kibbles in the bowl.
After few weeks I gave up and end up putting her on the Natural Balance potato and duck formula, half dry, half canned, mixing a spoon of tuna in to just get her to eat.
She is still skinny and I am still straggling, so I hear your pain
Good luck, Luda.