Friction occurs in BMX Freewheel
Yes that is as single speed freewheel and those two pieces should not stick
There are some serviceable freewheels (White) but they are expensive
Pretty sure you need to replace the freewheel
Based on the rust it looks old
If you remove it from the bike and it sticks then for sure you need to replace it
You can try spraying a lubricant in the grove but most likely the bearings are shot    

A freewheel is like $30 and it takes a special tool to remove
Take it to a bike shop
If you buy the freewheel from them the often install for free or a small fee  

Or check youtube for videos on how to do it yourself
The removal tool for a single speed is like $25 so not worth it unless you are going to do it a few times  

And if you are going to replace the freewheel then it is good practice to also replace the chain 

As Brian stated this can also happen from a chain to tight.
Chain should have a little play.
And crank the pedal a few revolutions - some times the chain can be more tight in certain positions