I experienced the same thing for about 2-3 weeks. After a day or two my stomach got so easily upset by any attempt of me trying to hack the phlegm out that I booted almost every attempt. It unfortunately took almost no effort to get the gag reflex going.

Soda Water/Club Soda/Ginger Ale provided some relief. Also you could try to space out the feeding to one can every 1.5 hours. Less chance of booting up a whole meal that way. I was using 8-9 cans of formula per day for ~2400-2700 Cals.

All I can say is it sucks but it will get better.