Is it worth getting an i7 7700k in 2018?

No reason to upgrade from an R5 1600. Even moving to the 8700k is a very minor upgrade. The 7700k from an R5 1600 is more like a sidegrade. Chances are you aren't even fully utilizing your 1600. Unless you're playing at 144Hz+ there is literally no reason to even consider going Intel.
 
if you are looking to game and stream, look at this article : http://www.tomshardware.co.uk/game-streaming-encoding-coffee-lake-ryzen,review-34144.html.

As the other posters have said, it's not an upgrade, more of s side-step. For streaming and gaming (simultaneously) the 1600 will be better(as long as you OC it to about 3.8ghz)