Feed as often as he wants. It will be very comforting for him and it is rapidly absorbed. Even if he was to chuck up his entire stomach contents as soon as he finished feeding, he would already have absorbed some.
Don't let out of hours or NHS24 tell you to stop breastfeeding. I got seen once by a nurse practitioner who told me to stop feeding ds for 24 hours and give "something like ribena" instead. ]
I complained.
Breastmilk is classed as a clear fluid and is NOT dairy!!
Hope he is better soon.