So I've had Chuck just over a week, and he is 9 weeks old. Part of the reason I got a puppy is to integrate with 2 house cats at an early age and after speaking with the breeder and asking for advice on here integration seemed possible as long as they are given enough chance to interact, and the cats set the tone as above him early on.

The interactions have not been great, mainly because there's so much room, and the cats have vertical leaping ability to escape. Chuck's first meetings clearly had playful intentions - he put his head down on the ground and was trying to show he wanted fun times. The cats ended up running away most of the time.

A few times Chuck cornered them and he has gotten smacked (which from everything I hear is good to set the tone as the cats being boss early on). However this has done nothing to increase the cats confidence, and they continue to hide away whenever Chuck is around, or straight up bolt away.

I'm a little concerned things aren't progressing as they should. When Chuck does see them, it's chase mode. And when he does corner them, it seems like he's barking aggressively.

It's only been about a week, but I see a lack of progression. Chuck is the only dog in the house, so I think it's important that Chuck and the cats at least have a working relationship, if nothing else but to quell boredom.

Any thoughts?

Time, lots of time. It took a while for our cats to get used to our puppy when we first brought her home.
For Chuck, I would suggest working on the leave it command. Start with treats and toys, then when he starts to sniff the cats tell him to leave it. If he does, reward him. if you bring him into a room where the cats are, maybe try working with a lease, have him attached to you so that he can't bolt after them, even if they run. If he sees them and gets ready, make him sit and calm down then let him calmy enter the room.
The cats will get used to him, and eventually they will snack him hard enough that he'll leave them be. Ours now, we have 1 who lives in the basement because she hates the dogs, so we leave her to her own devices. The other is the king of the house, and the dogs know it. They play together occasionally though, where Tika will walk up and nose bump him and he'll chase her away, repeat.

I'm not the worlds best trainer, but this was something we faced, so I hope it helps.

I have two cats as well and had to find a way to negotiate a peace treaty pretty quickly since we live in a studio apartment. Our situation is a bit different in that our male cat, Miles, can be aggressive. My biggest worry was that he would redirect aggression toward our female cat, Martini. Actually, what happened, is that bringing the puppy in seemed to unite them, common enemy I guess. Miles no longer bullies, swipes at and stalks Martini thankfully, but he is still plotting the death of the puppy on a daily basis. We frequently had to intervene between the two cats in the past, but they no longer scuffle.

In terms of Dizzy, I was actually more worried that he would get hurt than the other way around. Miles weighs about 17 lbs and Diz was 13 when he first came home. Miles was also ferrel, and when he feels threatened, he goes apeshit and will cause serious damage. Not just a swipe and run, a full on attack. I wouldn't let Dizzy approach him at all for about 2 weeks. The cats knew the dog was there and the dog knew the cats were there, but that was about it. He was very curious about them of course, and wanted to play with them, but until he was familiar with our apartment and where his space was, I didn't want to let him approach, I think he would have lost an eye. Once Dizzy got a bit bigger, I let him approach Martini, and she smacked him on the nose. He would stand a couple feet away from her and wag his tail and bark at her. I discouraged this, and would put him in a time out, I just felt like she deserved to be comfortable as well so I didn't want to allow that behavior.

My main goal between Dizzy and the cats was to teach him to ignore them. When he would start to fixate on them, I'd pull out the treats and clicker and work on him focusing on me. When he would make eye contact with me, click and treat. Once he figured out the game, the cats could have run up and smacked him on the butt and run and he wouldn't have flinched. I'm lucky in that he is extremely food motivated. When I felt a little more comfortable, I let him sniff Miles. Miles was on a piano bench (he felt safer because he was above Dizzy). Dizzy stuck out his nose to sniff and Miles clawed him, left a little scar on his nose. Dizzy walked away. Now, if either cat hisses, he'll walk away, sometimes he even goes in his crate lol. My other piece of luck is that neither cat runs from him, so they don't trigger his prey drive as much.

Dizzy has a habit I'm working to break where he lays on the floor and stares at them while wagging his tail, but that totally freaks both of the cats out, so I correct that behavior as well. Miles starts to go into attack mode and Martini starts hissing at him. He could just be laying on the floor staring at them, but they don't like it. I just do a simple "ah ah" and he stops. Its been a little over 3 months and the cats are comfortable moving around the apartment and Dizzy pretty much ignores them. That is the most I can hope for. I don't want allow Miles and Dizzy to play, because that can escalate so quickly and someone will get hurt, most likely both the dog and the cat and a human or two. We call Martini chicken little, because she gets scared easily and when she runs away from something she makes these quiet little meow sounds, like she's running and saying 'the sky is falling!' I wouldn't want to let him attempt to play with her, because I just imagine it would give the poor thing a heart attack.

On the other side of things, I have a squirt bottle with water always within reach and if Miles starts to act aggressive toward Dizzy for no reason, he gets a squirt. Miles doesn't like it when Diz and I play so he'll start to growl. Normally I just show him the bottle and he stops, but if he doesn't I squirt him.

Have your cats been around dogs before? I think your number one goal should be to teach chuck not to chase them and to ignore them if possible. That way if they want to interact and approach him they can do it on their terms without fear he will chase them or get them. Does he respond to your corrections? If not, teach him that as well. When Dizzy would do something bad and I would say 'ah ah' if he looked at me or stopped what he was doing, he got a treat. So I was rewarding him for stopping a behavior. I would also recommend keeping Chuck on a leash for the time being, until he stops chasing. The chase is his prey drive and allowing that to develop towards the cats is not good. Dizzy will chase other cats, but not ours, he knows they are off the menu/toy list. Just give them time. They are going to be annoyed and uncomfortable for a while and may never want anything to do with Chuck, or maybe you'll get lucky and they'll end up buddies. Cats are, well cats, so your best bet for keeping peace in the house is to teach Chuck they are not for puppies.

I think that's really good feedback. The cats have come out more over the last few days and they watch Chuck sleep sometimes now

Cheers

That's awesome! Ours are curious and watch Dizzy sleep too. Last night we had a bit of a breakthrough as well. Dizzy was awake laying on the floor in our hallway and miles walked by him and had to actually step over Dizzy's tail. Dizzy knew he was there but since I have been working on him not staring at the cats, he didn't look at miles and he felt comfortable walking by.