I think perhaps part of the issue is some of the travel blogs will tell you about using partners (ie: Alaska Air) to book AA tickets, but it requires "saver" award inventory. Similar to trying to use Korean Air Skypass miles to book "saver" with Delta flights. Since there is no more saver/award charts, you are basically forced to use KE or Alaska website and let's just say searching isn't the best (especially on Korean). Although the fact of the matter is that Delta never (or so it seems) releases "saver" business/first inventory to partners (although lately can't even find coach).

Perhaps the better question/answer is to find what fare class/buckets are required and possibly use Expert Flyer (although can't search a bunch of airlines anymore, so there goes that) to find flights?

But then again perhaps the OP is just asking for the cheapest flights?