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AA and LATAM are both members of the oneworld alliance (OW). LATAM has two types of availability, its own and what it publishes to its OW partners. To see if there's OW availability that you could call in to AA about, you need to search other using other OW partners. The simplest way, if you don't already have accounts with them, might be to use Award Nexus, which you can sign up for free (and do a number of searches for free) as a FlyerTalk member (click "more signup options" under the green Purchase button to sign up using your FT login). At AwardNexus, you can search via QF and/or BA (for OW flights such as LATAM), and you might want to search both. If neither shows the flights, then AA won't see them either if you call in. If at least one of them shows the flights, an experienced person at AA should be able to see them if you call in.

If neither QF nor BA show the flights, the only way to book is either to pay for the flight or to obtain LATAM miles (actually Multiplus points), but if you cannot use AA miles, then anything more you want to about transferring to LATAM miles or booking with LATAM miles, you should ask in the LATAM forum, rather than here in the AA forum. The LATAM/Multiplus English US website is kind of a mess right now (it's in a long state of transition), so you may need assistance with all that from the LATAM forum.