I can't comment on Kenya Airlines (although i did go through some reviews, I certainly wouldn't fly them), but what about Qatar Airways?
They fly to Nairobi and also from just about anywhere in Asia (and Melbourne as of December too).
Generally pretty cheap too (from Asia at least), eg I just put in some dummy dates for KL -> Nairobi in Feb and got $1080 AUD return.
Flew Qatar last month SIN-DOH-ATH and was please with all sectors, nothing went wrong at all really, a slight delay out of Athens due to ATC, but that's it, all bags were fine and staff friendly.
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Next Flights: 08/7 PER-DRW QF | 15/7 DRW-PER QF // 14/8 PER-MEL JQ | 15/8 MEL-PER JQ
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