I believe it should be something along the lines of “slah-vah oo-kra-ee-nee”

The “oo” part almost wants to be a “yoo” but doesn’t quite get there

the “kra-ee” almost slurs together into a single “kri” sound

And the “nee” almost drops off into “neh”

Disclaimer- I don’t really speak a word of Ukrainian, there’s a pretty big Ukrainian immigrant community in my area so I’ve been around Ukrainian speakers and heard it spoken probably slightly more than the average American, but I’m probably missing the mark on that a little bit.