Yes - that route is valid

There are a few things you need to be aware of - I think you now know them already:

• You are allowed at most two stopovers in your continent of origin - so of the stops you have - AMM, LON, MOW, AMM again - you have to decide which will be transits and which stopovers
• Your second visit to NYC - after EZE and before TYO - must be a transit
• Your visit to HKG must be a transit

You are using all 16 allowed segments (^), but you have not fitted in SCL which you said you would like in addition to EZE. If you don't want to go to HKG, then you can fly SYD-LON direct and so save a segment which you can use to visit SCL. Here's a routing for that
Krt-amm-JFK-lax-eze-SCL-JFK-NRT-del-NRT-sin-NRT-syd-LHR-DME-amm-krt

So - the next thing for you to think about is which frequent flyer program to accrue all the miles to. But that is a whole new topic of conversation