OK, couple quick options:
Using Star Alliance (United or US Air) here are some options out of chicago (you can us the same mileage to get to and from chicago at the beginning/end of this segment but it's just easier to find using Chicago instead of KC):
3/2
(SA)
UA895 Chicago(ORD) Singapore
13:20 01:30
+2 CHG 1 Economy 1 22:10
3/4
(MO)
SQ106 Singapore Kuala Lumpur
08:35 09:30 333 2 Economy 1 00:55
3/11
(MO)
CA972 Kuala Lumpur Beijing
00:30 06:40 757 M Economy 1 06:10
3/11
(MO)
UA850 Beijing Chicago(ORD)
17:25 17:35 777 3 Economy 1 13:10
Using AA miles and the same dates (and, again, starting in Chicago) you have a shitload of options:
10:35 1 Mar
ORD
15:05 2 Mar
PVG
American Airlines
AA0289
Economy
Only 7 reward flight seat(s) left in this class
17:25 2 Mar
PVG
20:15 2 Mar
HKG
Cathay Pacific Airways
CX0369
Economy
01:30 3 Mar
HKG
05:10 3 Mar
KUL
Cathay Pacific Airways
CX0791
Economy
2 flight connection, total journey time: 28 hours 35 minutes.
10:35 1 Mar
ORD
15:05 2 Mar
PVG
American Airlines
AA0289
Economy
Only 7 reward flight seat(s) left in this class
19:20 2 Mar
PVG
22:05 2 Mar
HKG
Dragonair
KA0897
Economy
01:30 3 Mar
HKG
05:10 3 Mar
KUL
Cathay Pacific Airways
CX0791
Economy
2 flight connection, total journey time: 28 hours 35 minutes.
10:35 1 Mar
ORD
15:05 2 Mar
PVG
American Airlines
AA0289
Economy
Only 7 reward flight seat(s) left in this class
18:20 2 Mar
PVG
21:05 2 Mar
HKG
Dragonair
KA0891
Economy
01:30 3 Mar
HKG
05:10 3 Mar
KUL
Cathay Pacific Airways
CX0791
Economy
2 flight connection, total journey time: 28 hours 35 minutes.
10:35 1 Mar
ORD
15:05 2 Mar
PVG
American Airlines
AA0289
Economy
Only 7 reward flight seat(s) left in this class
20:20 2 Mar
PVG
23:05 2 Mar
HKG
Dragonair
KA0809
Economy
01:30 3 Mar
HKG
05:10 3 Mar
KUL
Cathay Pacific Airways
CX0791
Economy
2 flight connection, total journey time: 28 hours 35 minutes.
10:35 1 Mar
ORD
15:05 2 Mar
PVG
American Airlines
AA0289
Economy
Only 7 reward flight seat(s) left in this class
18:50 2 Mar
PVG
21:35 2 Mar
HKG
Dragonair
KA0835
Economy
01:30 3 Mar
HKG
05:10 3 Mar
KUL
Cathay Pacific Airways
CX0791
Economy
2 flight connection, total journey time: 28 hours 35 minutes.
Inbound
Kuala Lumpur - Chicago - Monday 11 March 2013
Search up to 7 days earlierSearch up to 7 days later
Depart
Arrive
Flight Operating Airline
Class of travel
23:05 11 Mar
KUL
06:55 12 Mar
NRT
Japan Airlines
JL0724
Economy
Only 4 reward flight seat(s) left in this class
11:00 12 Mar
NRT
08:45 12 Mar
ORD
Japan Airlines
JL0010
Economy
Only 4 reward flight seat(s) left in this class
1 flight connection, total journey time: 22 hours 40 minutes.
17:45 11 Mar
KUL
21:30 11 Mar
HKG
Cathay Pacific Airways
CX0724
Economy
Only 5 reward flight seat(s) left in this class
01:05 12 Mar
HKG
06:15 12 Mar
NRT
Iberia
CX0524
Economy
Only 5 reward flight seat(s) left in this class
11:00 12 Mar
NRT
08:45 12 Mar
ORD
Japan Airlines
JL0010
Economy
Only 4 reward flight seat(s) left in this class
2 flight connection, total journey time: 28 hours 00 minutes.
I'm sorry that is messy as crap but I just copy/paste and that's how it spits it out, you should be able to decipher it.
There was some business/first availability in each program as well. The key if you use AA miles will be to find you availability for your MCI-ORD leg using AA's website and then use the BA website for the ORD-KUL leg. Write down the segments with award availability you want and then call AA and give them the flight info. They should be able to book for you from there. I am happy to help with this if needed. With AA miles it would 135k AA in First, 110k in business class, and 70K miles in economy all RT including the MCI-ORD segments.