flow in(to) (something)
To rush into something in a smooth, fluid manner, as of a liquid. We watched the tributary as it flowed into the river. I didn't consciously think of those images—it's like they just flowed into my head, and then I captured them in my poem.
flow in(to) something
to course into something; to pour into something. The words flowed into my head, and I felt like I could write again. The water flowed in when I opened the door on the flood.