How many meals is the Army suppose to provide barracks personnel not collecting BAH?

WTF? 1. BAH is for housing, separate rats is for food. 2, They are suppose to TRY to feed 3 meals per day. We got that in garrison, in training, we learned to tighten our belts.

SPC (Join to see) BAH is Basic Allowance for housing... so not applicable to your question.
Separate Rations is what is paid to service members authorized to mess separately ...IOW ion their onew, pay, time and schedule.
As for how many meals its three, that can be 3 in a DFAC, or 1 in DFAC, 1 MRE, one Hot A ration in the field, or 3 MRE, or any other combination of three meals provided to you. The requirement is nutrition and calorie count to keep the body going, the goal is palatable food, but the 1st one is the only requirement
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You're talking apples and oranges here. BAH is for housing. For food, if you are not receiving separate rations pay and are a meal card holder, then you eat in the DFAC and consume the food provided free of charge. 3 meals. Breakfast, lunch and dinner. That is the garrison way. In the field, if there is an MKT present, then you (usually) get two hots for breakfast and dinner and an MRE for lunch.