The LGA-KIN is a through flight with one stop - okay with one coupon. However there's no direct flight from KIN back to NYC, although there is another stopping flight to PHL. Otherwise KIN is via MIA.

For the N. America transcon in F it's hard not to recommend CX's flight between YVR and JFK. If you want to get to SFO and depending on the season, you could connect to QF's 744 (with FC) SFO-YVR leg. A possible N. America routing might then be HKG-JFK//LGA-KIN-MIA-DFW-SFO-YVR-JFK (ending in NYC) or HKG-JFK//LGA-KIN-MIA-JFK-YVR-SFO-YVR if you want to end up in YVR for BA's London flight and don't need to include Texas. Other riffs possible.

As for the double Europe entry issue, the rules are pretty explicit - only on a <24h transit to/from Nigeria, Ghana, Kenya, Tanzania and Uganda. Not Mauritius, not SA.

If you want to end up in west Africa, note that ABJ only seems to be served by SN, which is not a OW airline thus ineligible. Looks like the closest you could get would be ACC from London. ACC would be eligible for the second Europe entry, so if you did your Europe segments at the beginning, you could go Africa - Europe - Asia - N. America - xLHR - ACC within the rules. Doing Kiev etc at the end would not be kosher.

If by any chance you're using the RTW planning "tool" (rhymes with "fool") from oneworld.com, don't.

And welcome to FT!