plastic bag ban in Kenya

This article from the BBC website uses the term "carrier bag", which is not what a ZIP Lock bag is. So I don't think tourists will be in trouble for having some ZIP Lock bags in their luggage.

A carrier bag is what you get at a supermarket.

We saw a bunch of little boys in Kenya playing soccer with a ball made of hundreds of plastic bags rolled one on top of the other to a (sort of) ball shape. Made us want to weep.

There is a similar ban in Rwanda (and in many US communities). No one went through my packed luggage to see if I had any zip locks (which I did!). They were looking for plastic bags being carried by people.

Ikea (and probably others) sells a sturdy but very lightweight grocery-style bag with two handles. It crushes down to a tiny ball but is strong enough to carry more wine bottles than you need for the day.

While respecting their plastic carrier bag ban, perhaps give a moment to waste in general. It reduces weight in your luggage, and also trash in Africa, if you remove commercial packaging at home where you can discard or recycle it. In Africa, there is little to no recycling which has led to this bag ban. I thought it made great soccer balls, but it blows across the country as waste or it gets burned - which is toxic. Bottled water is common and hard to get around, but most 'permanent' tourist camps have water purification systems, so consider bringing your own reusable bottle to reduce plastic waste. Some tourists go to the effort of cutting up their plastic water bottles and bring it home where recycling is available. There are some efforts in big cities to create glass and plastic recycling systems, but it isn't common practice for drivers or tour companies to make the effort to bring back the empties to the city to recycle.
I volunteered in Tanzania for a while and watched the 'mommas' gather garbage during their daily sweep, then start a little fire. Burned the garbage and while the flame was hot, cooked up the next meal (rarely lidded). Plastic bags, metal, paper, anything that would burn or melt. I tried to rationalize that the month I was eating those meals wasn't enough exposure to the toxins to make me crazy or develop cancer, but I did wonder how the mommas were fairing after a few years.