In a word, no. There is talk of an East African Visa or that one visa from one of the countries will get you into the whole of east Africa, but i guarantee if you got to those two borders you will be met with a blank expression. I cannot even tell you if such a visa even exists, I have heard talk of it but never, ever seen someone who actually had it and with where I am based (Uganda) you would think that you would have at least seen one after these years - i would be delighted to hear first hand that it is available though as it would save a lot of people a lot of time!
The borders are very easy, just turn up with your $50 or whatever it is, fill in the forms and you're done.