Here's one option at $2,361 - the least expensive route I found that will earn you the miles you're looking for:

Austin (AUS) to Berlin (TXL) - Fri, Dec 20
American Airlines Inc. Austin (AUS) to Dallas/Fort Worth (DFW) - Fri, Dec 20
American Airlines Inc. 2230 Dep: 11:55AM Arr: 1:00PM 1h 5m MD-80 Economy (H)
Layover in DFW 3h 45m

British Airways p.l.c. Dallas/Fort Worth (DFW) to London (LHR) - Fri, Dec 20
British Airways p.l.c. 192 Dep: 4:45PM Arr: 7:25AM 8h 40m Boeing 747 Economy (H)
Layover in LHR Sat, Dec 21 1h 10m

British Airways p.l.c. London (LHR) to Berlin (TXL) - Sat, Dec 21
British Airways p.l.c. 992 Dep: 8:35AM Arr: 11:25AM 1h 50m Airbus A320 Economy (H)



Berlin (TXL) to London (LHR) - Thu, Dec 26
Air Berlin PLC & Co. Luftverkehrs KG Berlin (TXL) to Gothenburg (GOT) - Thu, Dec 26
Air Berlin PLC & Co. Luftverkehrs KG 8300 Dep: 5:25PM Arr: 6:40PM 1h 15m Boeing 737 Economy (H)
Layover in GOT 0h 55m

American Airlines Inc. Gothenburg (GOT) to London (LHR) - Thu, Dec 26
American Airlines Inc. 6267 Dep: 7:35PM Arr: 8:40PM 2h 5m Airbus A320 Economy (H)
OPERATED BY BRITISH AIRWAYS P.L.C.


London (LHR) to Austin (AUS) - Sat, Jan 4
American Airlines Inc. London (LHR) to Dallas/Fort Worth (DFW) - Sat, Jan 4
American Airlines Inc. 79 Dep: 1:25PM Arr: 5:40PM 10h 15m Boeing 777 Economy (H)
Layover in DFW 1h 50m

American Airlines Inc. Dallas/Fort Worth (DFW) to Austin (AUS) - Sat, Jan 4
American Airlines Inc. 2399 Dep: 7:30PM Arr: 8:30PM 1h 0m MD-80 Economy (H)


Cost per passenger (including taxes & fees) $2,260.80
Total cost for 1 passenger $2,260.80