The pink flesh is fine; the rest of the slice is not
A kitten can eat watermelon in a very specific form: ripe pink or red flesh, cut into a small cube, with dark seeds picked out and the green rind and pale rind layer trimmed completely away. Served that way, a bite or two is a harmless novelty on a warm day. Served as a wedge she can gnaw freely, watermelon becomes a problem, because the parts she would reach next are the parts she should not eat.
Cut her cube from the centre of a slice, well away from the rind, and check it twice for seeds, including the small pale ones that hide in the flesh.
A juicy treat she experiences differently than you do
Watermelon is mostly water, which is why it reads as refreshing, and its soft flesh is easy for a kitten to mouth without chewing effort. Interestingly, the quality people prize in it is largely lost on her: cats lack the taste receptors for sweetness, so she is responding to the cool, juicy texture and the novelty of its scent, not to a sugary thrill.
Nutritionally the cube contributes fluid and little else, which is fine for an occasional bite. In larger amounts the water and natural sugars together tend to loosen a kitten's stool, and fruit should never crowd her bowl at the expense of the protein-rich food she is growing on.
Trimming and serving a kitten-safe cube
Start with a ripe melon, wash the outside before cutting so the knife does not carry surface grime into the flesh, and slice her piece from the seed-sparse centre. Remove every dark seed you can see and trim all rind, including the firm pale layer just under the green skin, since rind is tough, hard to digest, and a choking risk in chunks.
Offer one small cube, roughly thumbnail-sized, on a saucer rather than the lawn or floor where she might drag it and guard it. Skip frozen watermelon for a kitten: rock-hard frozen fruit is rough on small teeth and mouths, and room-temperature or lightly chilled flesh gives her the texture without the hazard. Watermelon drinks, sweets, and flavoured ice treats made for people are not the same food and should not be shared.
Signs she has had enough melon
One cube rarely troubles a kitten, but watch for the usual fruit feedback: soft stool later that day, a gassy belly, or vomiting if she managed to chew rind before you noticed. A kitten determined to eat the rind of a discarded slice is the common route to trouble, so melon scraps go straight into a closed bin rather than the counter edge.
Contact your veterinarian if she swallows a chunk of rind and then coughs, gags, strains, or goes off her food, or if diarrhoea lasts beyond a day. Otherwise, an enjoyed cube with normal digestion afterwards simply joins her list of approved novelties.
Jotting the result into KinsLe through Care Teams means the next person slicing melon for the family already knows her rule: flesh only, seeds out, one cube, rind straight in the bin.