Hi...he should doing it the same way you have described but should not be banging too hard and it can cause haemorrhage internally in such an young infant. I suggest doing it in a gentler way.
By the way - being born a premie and weighin 10.5 pounds by 4 months is excellent weight gain. I congratulate you on that.
Hope my answer was helpful for you. I am happy to help any time. Further clarifications and consultations on Health care magic are welcome. If you do not have any clarifications, you can close the discussion and rate the answer. Wish your kid good health.
Dr. Sumanth MBBS., DCH., DNB (Paed).,

Hi
welcome to HelathCareMagic

Infants swallow air during feeding, and burping is encouraged to prevent gaseous distention of the stomach.
Proper way to burping is pat back of baby gently till he burps while holding baby against your chest/shoulder, baby's chin rest on your shoulder while you support him with one hand and burp him with the other.You can sit or stand while doing this. This is most common method of burping.Point to remember is it has be gentle , even rubbing back can be sufficient.
You can also burp baby by making him sit in your lap , point is avoid neck flexion, and proper support of back and shoulder or putting him back in your lap and gently pat or rub ,head has to higher ,make sure you are not holding neck of baby as it may make breathing difficult.
Key message is proper position and to be gentle.
Hope I answered your query,
Feel free to ask if any other query
thanks