It's an absolutely terrible use of miles, but to maximixe your potential gain to the "lifetime counter":

AAdvantage Miles --> Diners Club
10,000 miles --> 5000 Diners Club
Limit: 50,000 AAdvantage Miles

AAdvantage --> Hilton
5,000 Miles --> 10,000 HHonors
Limit: 150,000 miles per year

AAdvantage --> Priority
5,000 Miles --> 4,000 Points
Limit: 150,000 miles per year

150,000 Miles to Diners Club
150,000 Miles to Hilton
50,000 Miles to Priorty Club
=====> BURN 350,000

Transfer and get: (according to WebFlyer)
25,000 Diners Club Points --> 25,000 AAdvantage Miles
300,000 HHonors Points --> 45,000 Advantage Miles
120,000 Priorty Club Points --> 30,000 AAdvantage Miles

You end with 100,000 miles after 350,000 miles burned, a net loss of 250,000 miles.

So, basically, in exchange for burning 250,000 miles, you can up your lifetime counter by 100,000. Not really worth it to me, but I suppose for some trying to hit that status, who knows...