It sounds like your new family member is adjusting pretty well, actually. Kittens are active, so as long as they are active & doing well I wouldn't worry so much. However, you may have what I like to call a 'grazer'... Eats a bit, goes on & does some stuff & then comes back for a few more kibbles... repeat... So it will be important to make sure that he has food available at different times or all during the day & night. I know that can be difficult with dogs, but you may want to start working with him & the dogs to make sure his eating area is readily available away from dogs?
I didn't ask, but age may have alot to do with his eating volume, too, as well as food type. My hubs & I have fostered for many years & I have found that when they get a 'growth spurt' they eat ALOT, but other than that (unless they are sick) they tend to eat 'regularly' - a bit when they wake up, in the morning & at night when all the dogs are eating, when we yell 'treat' for treats, etc...
If you have any issues or questions this is a great forum to ask. You can also rely on the rescue or you shelter you adopted from and sometimes from the person you adopted from, not to mention your vet. I have found that if anything 'emergency' happens I can call the vet (or emergency vet) on the phone & often get 'talked through' an issue or a worry prior to bringing them in - it settles my mind & heart!
If you worry that your baby is not eating enough, try a different food & always, if available, feed him a good quality kitten food. If he is losing weight or becomes less active, fevered, clingy (more than usual), or sick - get him in to see the vet. And make sure to get him in on his regular vet appointments, especially the first two years (shots are important, rabies, etc). If you do decide to change his food, mix in a little for a few days so that he doesn't get diarrhea or an upset stomach, but don't be surprised if he does get loose stools for about a week - babies tummies can be sensitive, but don't let that deter you from making a change if it benefits him!
You are doing a great job - keep it up!