As noted above, BA does have an interline agreement with KQ. If these flights are on one ticket then you should be able to check through. In practice, it may work out differently.
Results from https://www.ExpertFlyer.comInterline Agreements:
Flying BA

E-Ticket Interline Agreements
AA AC AE AF AH AI
AM AS AT AV AY AZ
BD BE BI BL BM BP
BR BT BW B6 CA CI
CM CO CX CZ DL DT
EC EI ET EY FB FC
FI FJ FV GA GF GK
G3 HA HG HM HP HU
HX IB IG JC JJ JL
JM JP JQ JU JY J2
KA KC KE KK KL KM
KP KQ KU KX LA LG
LH LI LM LO LP LR
LX LY MA ME MH MI
MK MN MS MU MX NH
NU NZ OA OK OM OS
OU OZ PG PR PS PU
PW PX PZ QF QI QM
QR RB RJ RO SA SB
SN SQ SU SV SW S7
TA TF TG TJ TK TM
TN TP TU UA UK UL
UP US UU U7 VK VN
VS VY WM WS WY XK
XL 2K 3K 3U 4C 4M
4O 9B 9W



Paper Ticket and Baggage Interline Agreements

MAY ISSUE TICKETS INCLUDING
AA AC AE AF AH AI AM AS AT AV AY AZ A3 A9
BA BD BE BI BL BM BP BR BT BW B6 CA CI CM
CX CZ DL DT EC EI EK ET EY FB FI FJ FV GA
GF GK G3 HA HG HM HP HU HX IB IC IG JC JJ
JL JP JQ JU JY J2 KA KC KE KK KL KM KP KQ
KU KX LA LG LH LI LM LO LP LR LX LY ME MH
MI MK MN MS MU MX NH NU NZ OA OK OM OS OU
OZ PG PR PS PW PX PZ QF QI QM QR RB RJ RO
SA SB SN SQ SS SU SV SW S7 TA TF TG TJ TK
TM TN TP TU T0 UA UK UL UP UU U0 U7 VN VS
VY WB WF WM WS WY XK XL XM X5 2K 3K 3U 4C
4M 4O 5T 7H 9B 9W

MAY CHECK BAGGAGE TO
AA AC AE AF AH AI AS AT AV AY AZ A3 A9 BA
BD BE BI BL BM BP BR BT BW B6 CA CI CM CX
CZ DL DT EC EI EK ET EY FB FI FJ FV GA GF
GK G3 HA HG HM HP HU HX IB IC IG JC JJ JL
JP JQ JU JY J2 KA KC KE KK KL KM KP KQ KU
KX LA LG LH LI LM LO LP LR LX LY ME MI MK
MN MS MU MX NH NU NZ OA OK OM OS OU OZ PG
PR PS PW PX PZ QF QI QM QR RB RO SA SB SN
SQ SU SV SW S7 TA TG TJ TK TM TN TP TU T0
UA UK UP UU U0 U7 VN VS VY WB WF WM WS WY
XK XL XM X5 2K 3K 3U 4C 4M 4O 7H 9B 9W