When I had my baby in the NICU they often put him on his belly and on his side. Of course he was constantly monitored. I always thought it was odd that they did this, but this hospital was one of the top NICUs in the country....I don't think they would do anything to hurt the babies there.
Of course I meant that she should monitor her baby while he is on his tummy. Having him rest prone on her chest is ok...I don't think I've heard about any connection with that and SIDs.
They used a tightly rolled blanket behind the baby to support him on his side when he was in his crib and I did the same when I took him home. He almost would never sleep unless he was on his tummy either because that's almost all he did when he was in the hospital. I just had to make sure that the surface was firm and that it would never block his airway. I never left him like that say, on my own bed...only in his bassinet, which is very firm....and I always kept an good eye on him.
Our house is smoke free too, which is one of the leading causes of SIDs.
I was wondering if some moms whose babies die of SIDs put their babies on cushy surfaces, instead of something that is firm and that blocks the baby's airways when they are face down.
Anyhow, the OP could also let the baby sleep in a carseat. Every one of my children except my son who was in the NICU have preferred their carseats. There is no danger on SIDs or choking on spit up that way, and when they have a cold and congestion, it's easier for them to breathe. They also get less gaseous.
She can also try baby gas drops or gripe water.