How can I install a front brake on this kids bike? Coaster brakes are dangerous and confusing but they keep shipping kid bikes with them for some reason. How can I add a front brake to this bike?
Do not install a front brake to a bicycle that has not been designed for front brakes!!! A front brake requires a frame strong enough for front brake and a fork strong enough for front brake.
There is a quite popular bike sold in my area called Helkama Jopo. It used to be a coaster brake bike with no front brake.
Then, at some point of time someone working for Helkama thought it would be a good idea to switch the steel material of the frame to aluminum, and at the same time install a front brake. Unfortunately they did not design the frame to withstand the loads of a front brake.
The bikes started to fail (the frames cracked and separated in half during use). Some failures resulted in tremendously hurt riders injured for the rest of their life.
The manufacturer claimed that these failures were the result of incorrect use, i.e. jumping and doing wheelies with the bike. Not so!
There is a post in LinkedIn by a mechanical engineer analyzing the issue: https://www.linkedin.com/pulse/miksi-jopo-hajosi-vesa-tiainen
Unfortunately the post is in Finnish, but the mechanical engineer showed that the failures were not due to incorrect use such as jumping and doing wheelies, but they were caused by the manufacturer's decision to install a front brake.
The manufacturer probably realized the mistake, and later front brake versions of the bicycle contained a slight alteration in the frame to prevent peak loads.
The manufacturer still today lies that wheelies and jumping were the cause even though they did a fix to the frame to allow front brake usage, and thus clearly understand that front brake caused peak loads in one part of the frame.
Your frame seems to be exactly the same type as Helkama Jopo, i.e. there are no separate top tube and downtube attached to the headtube. Instead, the top tube and downtube meet earlier and the unified tube attaches to the headtube. This design has exactly the same flaw as the Helkama Jopo design.
Your frame is not strong enough to withstand front brake loads!!!