Coming to this thread late so not sure I will be of help or not.
I nanny for a 4.5 month old so similar aged child. Mum has gone back to work so baby has no choice but to take a bottle from me. First couple of weeks, she refused to have more than about 2oz per feed and would only feed once very distressed.
This week has been much better though. The things that have helped I feel are:
Used No.2 size teats - Avent. (stick with a brand of teat so that baby gets used to it. NUK has a teat that is shaped differently to other brands, so that one can work well sometimes.) Check the flow, two holes I've found to be good, as milk flows without baby sucking too hard.
This particular baby likes milk hot. Formula milk made up from powder with near boiling water, then cooled a bit under cold water but not too much as she likes it hot. Experiment with milk temperature, surprising how hot some babies like it.
It takes time for a nanny and baby to tune in to each other. After a few weeks, nanny should be better at spotting the signs that baby is hungry, tried, is wet etc.
This past week, baby I care for has had two 12oz days, whereas before she was only taking 6, 7oz during a 12-hour period. So stick with it, baby will get used to it.
Breastfeed at other times. My boss BFs whenever I'm not there and will BF before leaving in the morning.