Well, I can tell you how we successfuly introduced a 14 month old cat that had never lived with a dog to three dogs that had never lived with a cat and wanted to chase every cat they saw...
We started with a stairgate between the living room and the hallway and the cat did stay upstairs initially, but although we kept dry food upstairs for her, we started giving her abit of wet fod and then gradually moving that downstairs closer to the dogs, only moving it when she was happy with where she was. She eventually started to realise that the dogs couldn't get near her and eventually would go quite close to them. It jhelped that our dogs will 'leave' on command and if they paid undue attention to the cat we distracted by saying 'leave' and giving a treat when they did. I did also hold the cat near the dogs a few times, but only what she was happy with.
Once the cat was hapy being near the dogs, we got the dogs on leads (just in case) and shut the cat int he living room with us and then brought the dogs in. We did bring one in at a time to start with. The cat would initially stay up her cat tree and ignore the dogs. Again, we rewarded the dogs for ignoring her.
Eventually the cat realised they couldn't get her and started to mosy past them. Once the dogs were completely ignoring her we let them in the room and off the leads. They did try and approach her and have a litle sniff, but a 'leave' made them come away. She did hiss at them a couple of times when they approached her, but that was it.
I supppose at any time had the dogs got too excited or the cat been distressed, we would have gone back a step.
We have since got a kitten and although the dogs got excited at first as they knew it was a different cat, we never had any problems and the youngest dog and kitten (now seven months old) play together quite a lot, which is great to see. The cats are house cats and they just go about their business ignoring the dogs and the dogs do the same. Our dogs would still try and chase any outside cats if they got the chance, I suspect and I always make sur ethe dog and cats dont' have access to each other if I am out. I really doubt anything would happen, but dogs are dogs at thend of the day, and it's not worth the risk.
Oh, I used the same brush on the cat as the dogs too. Apparently cats work a lot by smells, so maybe you could give the dog a blanket and then give it to the cat afterwards, still smelling of the dog? You can also get a thing calle d'Feliway' a cat appeasing pheremone spray that might help.
Hope this helps a bit.