Can I use functional gray paint with oak trim in a small bathroom

Hi Linda,
Yes of course, I seen a similar thing a few times and it looks great.

Make sure to use a good waterproofing substrate or under coat behind it too. I agree if you already have the trim and it's stained, it would be a shame to paint over it, as new oak trim is very expensive.

Linda, you might find useful information here: https://www.pinterest.com/explore/oak-trim/