Not convinced it's worth the effort TBH. You can always sprinkle probiotics on their food or mix into a little juice. And eventually give them capsules to swallow.
I wanted yogurt for a recipe- a biscuity pastry made with yogurt - so I experimented!
Recipe:
Reserve a tablespoon of Oatly cream, and heat the rest to 42C. I use my digital meat thermometer.
Mix the contents of 1-2 acidophilus probiotic capsules with the reserved Oatly, then pour the heated Oatly on to it and mix well.
Put the mixture in a sealable pot or two, in an insulated container. I put a warm hot water bottle in a picnic bag, and put the yogurt inside the bag in a nest of scrunched-up newspaper, You could use a yogurt maker, I'm sure, or put it somewhere warm like the airing cupboard.
Leave undisturbed for 24h, then transfer to the fridge and leave for another 3 days or so. It thickens up and develops a yogurty lavour. It keeps really well, a couple of weeks in the fridge.
I've never flavoured the yogurts, but I'm sure you could do that adding jam/honey/chocolate powder/anything either at the very beginning when you mix it up, or at the very end when you serve it up.