If hes a guzzler it is best that you give him a few mins feeding then stop and burp him,do it frequently sometimes they do guzzle and they take in a lot of air..and that hurts ,cereal for a 3 month old is not a good idea and it will make him yell more, hes possible eating too much not too little .With burping its always good to hold him with hand on his chest tipped slightly forward , don't pat, stroke his back firmly with the other hand .Remember what I have said he needs burping more ... good luck
Can you get a good weight on him? If he's losing weight, I don't think you'd have trouble getting a pediatrician to move him to the top of the list - that's an emergency.
Does he appear to be dehydrating? (No real tears when he cries, fewer wet diapers).
Is he still having normal bowel movements every day?
my first baby was born 4 weeks early and had significant feeding issues (although they are not only common in preemies- term babies may have them too). It actually got worse as the weeks passed. She had a weak s.uck and also had poor coordination of the suc.k-swallow-breathe pattern. We had to try every bottle system under the sun before finding one that helped. We ended up on the Nuk orthodontic nipple (the older, narrow style). Because the hole is on the top, the milk didn't shoot down the back of her throat when she paused to catch her breathe. The firm base made it easier for her to latch back on when she had to release to catch her breathe.
I would suggest you keep trying different styles. Also, try different flows. If he is choking, then the flow may be too fast. If he is getting frustrated, the flow may be too slow. At 3 weeks old, he should be on either newborn or slow flow.
Or... there is another possibility
My second also had significant feeding difficulties, although for different reasons. Her reflux was so terrible, feeding her was an absolute nightmare. She didn't have the puking kind of reflux, but silent reflux where she would swallow everything back down. Still she had the classic signs of reflux- the screaming with burps, arching her back, etc.
Of course, there are many other possible explanations- those 2 are just my experiences. But in both cases, I did need the help of professionals. I agree with Rockrose, that you need to watch and make sure he is gaining properly and not getting dehydrated. I would definitely NOT give him cereal, especially since you don't know what is going on. That would fill his tiny tummy, but cereal is neither nutritional or hydrating and can cause even more problems at this age.