Flight in South America is expensive. I have travelled to the region 7 times now and I found that internal flight in the region is expensive. The problem is not many competition in the area. There are only LATAM (merger between LAN and TAM), Avianca and Aerolinas Argentina for major airlines. There are smaller airlines like Sky or Gol but still they are also expensive. Again, it’s about less competition in the area. I’m not sure booking early would help. I usually travelled to the region in Nov or christmas time and I booked flights in Jan but the price difference is negligible.
You probably can use Avios on LATAM but I doubt the availability is there if you try to book regional flight. If you fly within Chile, might be worth looking at LATAM pass. Also, what I found is travelling one way is really expensive even for short haul so if you can, try to book return trip.
Good luck on your planning. I might be biased since I love South America but the cost will worth it.