I think he can totally feel emotions, just that without a soul he lacks natural connection to those emotions, especially compassion/empathy.
I’d imagine it being like your body suddenly forgot how to breathe on instinct and suddenly every breath you had to take was a conscious action. But by the end of the game I think Flowey learns how to feel compassion again even without a soul to ground him.
the experience changed him to be invested in others happiness.
It just takes a lot of time and experiences to relearn how to “feel” again.