Be careful with that return routing. ATL-LAX-MIA are the same flight number as are MIA-DFW-ICN. You should be OK getting miles for the first two legs since same flight numbers in different directions is pretty common on AA now. But, the MIA-DFW-ICN should only credit as MIA-ICN. The difference isn't that great, but if you need every mile to requalify you need to account for it.
American Airlines – Flight 2471 (economy) 4h 44m
7:10p Wed, Apr 29 ATL Atlanta, GA
8:54p Wed, Apr 29 LAX Los Angeles, CA
Boeing 737-800 (Narrow-body Jet) | 4h 44m | 7 seats remain
Same plane LAX Los Angeles, CA
0h 56m
American Airlines – Flight 2471 (economy) 5h 04m
9:50p Wed, Apr 29 LAX Los Angeles, CA
5:54a Thu, Apr 30 MIA Miami, FL
Boeing 737-800 (Narrow-body Jet) | 5h 04m
Change planes MIA Miami, FL
1h 14m
American Airlines – Flight 281 (economy) 3h 07m
7:08a Thu, Apr 30 MIA Miami, FL
9:15a Thu, Apr 30 DFW Dallas, TX
Boeing 737-800 (Narrow-body Jet) | 3h 07m | 7 seats remain
Same plane DFW Dallas, TX
1h 30m
American Airlines – Flight 281 (economy) 14h 30m
10:45a Thu, Apr 30 DFW Dallas, TX
3:15p Fri, May 1 ICN Seoul, South Korea
Boeing 777 (Wide-body Jet) | 14h 30m