How could I prove I'm still married to me my wife? I could prove I wasn't if I had divorce papers, but how would I prove I am?
IOW, you are asking for something that does not exist.
Now they are likely documents tending to show that a marriage still exists, like joint tax returns, joint bank accounts, cencus records etc. Probably none of them, save maybe a cencus record, would apply in 1961 Kenya.
The guy was a Muslim, he could have just said "I divorce thee", three times, and he no longer be married to "that woman".
That’s the point. There’s no proof. Only allegations, assumptions.