Looks like botrytis, and it may be spreading up the stem. I'd try to cut them off, if practical.

Thanks for the reply!

I've been checking my raspberry plants, the brown flower buds are still there, but they haven't spread. This really started happening when it raining a lot for two consecutive days. Now the weather is dry. I'll remove the brown ones.

Glad to hear it's not turning into a problem. I noticed last year on my red raspberries that some of the ones that looked like that, eventually spread up the stems to other flower buds too. This year, so far, they've been ok.