The oat milk is fine; the saucer routine is not
Oat milk itself is a gentle drink for most dogs. Made from oats and water, it contains no lactose, which is the part of cow's milk that upsets many adult dogs, and a few laps of the plain kind are unlikely to trouble a healthy dog. The problem in your scenario is location, not the oat milk. A saucer under a coffee cup is a saucer that also holds coffee drips, and caffeine is genuinely harmful to dogs, affecting the heart and nervous system. A dog trained to lap from your saucer will lap whatever lands there, so the habit should change even though the headline ingredient is benign.
Which oat milks pass and which stay yours
Plain, unsweetened oat milk is the version to share in small amounts. Many flavoured and barista-style oat milks carry added sugar, oils, and flavourings that add empty calories, and chocolate oat milk is firmly off the table because cocoa is toxic to dogs. Check any sweetened product for xylitol, also called birch sugar, an ingredient that is extremely dangerous for dogs and appears in some human sugar-free drinks. Homemade oat milk or a simple commercial carton with a short ingredient list is the safest choice, and if the label is crowded with additives you cannot identify, keep that carton for your coffee only.
A bowl-sized portion, not a saucer habit
Pour a small splash, roughly a couple of tablespoons for a medium dog and a teaspoon or two for a small dog, into his own bowl as an occasional treat, ideally not every day. Oats bring soluble fibre, which in larger volumes can produce wind or loose stools, so the first serving should be the smallest and followed by a day of observation. Never let him finish your coffee to reach the oat milk at the bottom, and move cups out of reach when you leave the room, because a committed saucer-lapper will go straight for a cooling latte on the side table. Dogs with grain sensitivities or on a vet-supervised diet should skip oat milk until you have asked at their next appointment.
Signs the morning ritual needs a vet's view
If you make oat milk at home by blending and straining oats, the plain strained liquid is the version to share, served fresh rather than after days in the fridge. The leftover oat pulp is sometimes offered to dogs too, but it is concentrated fibre, so a teaspoon stirred into food is plenty and a bowlful invites the loose stools you were trying to avoid.
After any episode involving actual coffee rather than oat milk alone, watch for restlessness, trembling, a racing heart, vomiting, or unusual agitation, and contact a vet or emergency service promptly if those appear, since caffeine effects can escalate. For oat milk alone, the expected worst outcome is mild digestive looseness that settles within a day; persistent diarrhoea or vomiting after any new food deserves a call. Most households solve this permanently by giving the dog his own small morning ritual, a splash of oat milk in his bowl while you drink your coffee in peace. Recording the no-cups rule in KinsLe through Care Teams means guests and family all protect the same boundary instead of undoing it with one offered saucer.