This sounds like a security issue for your kitten. This behavior won't cause your kitten emotional harm, so please don't worry about that. If your dog doesn't mind, it should be alright for your cat to continue this behavior, and he should outgrow the behavior as he gets older. The only concern would be ingesting hair from your dog and/or being exposed to anything dangerous or toxic which your dog may have come in contact with on the belly area, outside or inside. If your kitten is ingesting dog hair, this could cause a dangerous intestinal obstruction, so keep an eye on his urination/defecation.
Your kitten may have been weaned or separated from his mother too early, and that's why he's exhibiting this behavior. Instead of offering food/water, when your kitten does this, try distracting him with toys or give him a safe object to suckle on, instead (plain cotton material, nothing fuzzy). Some kittens have a stronger sucking reflex than others and this behavior follows them for a while.
If your kitten doesn't feel comfortable with you holding him while you're sitting, don't force him to. Hold him standing up and then put him down when you sit. He may have some anxiety and feel more 'trapped', like he can't get away, when you're sitting. Some cats are just not lap cats; mine isn't, but he's extremely affectionate, and also likes to be held while I'm standing.
Try a cat appeasing pheromone called Feliway/Comfort Zone for Cats, which helps to relax stressed or anxious cats, and is useful in a multitude of situations. It comes in both a spray and plug-in diffuser, available at major pet supply stores like Petsmart, and also online. The diffuser resembles a plug-in air freshener, but has no scent to humans. For more information, please see: www.catfaeries.com/feliway.html