Hi
We took on a rescued Springer and a few months later got a 7 week old kitten. The dogs have always had the dining room, kitchen, lobby area which leads to a large dog flap into the garden.
When we brought the kitten home, she was allowed upstairs (somewhere that the dogs are not permitted to go) and we kept a litter box on the landing for her so she didn't have to run the gauntlet to go outside (after jabs obviously).
In the early days, I couldn't imagine that she would ever go past the dogs as Ollie used to pounce on her every time. She eventually hissed at him a couple of times and swiped him round the chops and established herself as the definite boss in our household

- They now get on great and she rubs herself all round Ollie - he still trys to pounce on her occasionally but she puts him firmly in his place.
At the time it seems as though it'll never work but with a bit of time I'm sure it will be fine. I would try to give the cats an area that the dog can't go to give them a bit of security.
Good luck