Chain jumping, unsure why The chain likes to jump from the front sprocket, it is my impression that it makes no difference if the chain lies on the inner or outer cogs. Since I am unsure about the root cause I ask here for some pointers to troubleshoot the issue.

Bike:

The bike in question is an old 20" kid bike from a garage sale, history is unknown except that it is at least 7 years old. Former maintenance was neglected. It has an 1x6 transmission. The entire transmission is rather old and not the fanciest one. I do not have much experience adjusting the derailleur but in the end I was able to change smoothly to every gear (adjustment was done with the bike upside-down). The chain is well lubricated and has no stiff links. The entire transmission (front/rear sprockets, pulleys) moves smoothly. 

Observations:


Observing my son riding the bike on the lawn I see the chain jumping a bit too much for my liking (amplitude about 10cm), I am not sure if that is fine.
When I tried to reproduce the issue I was able to "block" the chain between one of the rear sprockets and the jockey (upper pulley), I presume the issue was missing clearance between them. AFAIK there is no option to adjust that distance nor the spring tension.


Update

Closer inspection revealed that the large rear cog is definitely worn: The rear cassette will be replaced.

Update #2

I replaced both cogs, chain and derailleur (including cables). The chain behaves a bit better but still jumps from time to time from the front cog. The chain had a stiff link where I joined it, but that got resolved. The new front cog has no wobble. The rear derailleur is properly adjusted (smooth shifting to every position).

Frankly, I have no idea on how to proceed (Will post pictures of the new setup).
Perhaps I should mount a chain guard?

Additional thought: My son is just learning to shift. Perhaps I am overthinking that issue. Could it be that misuse (perhaps he is playing with the shift lever while standing) provoke most of the chain jumps? If so, would a chain guard limit the impact?
There are a few reasons that might cause the jumping of chains.


Chain or sprocket is worn out (Buy new ones).
The derailleur is misaligned (Needs adjustment).    
The wheels are not fitted properly making it a bit slanted (clean the crevices
and fit the wheel properly).


Check all of these and comment back if all are good.