Hello, I'm Dr. Bob. I've noticed your question in the queue for some time and decided that you deserve an answer, although it may not be one you wanted to hear. Animals are complex unpredictable creatures - that's what makes them so interesting! But without having observed both your dogs as well your parakeet for some time, to get an idea of their particular personalities, I wouldn't begin to advise you to even attempt this "assimilation". Birds can be curious, self-protective, or even aggressive, and dogs can react to their actions in ways that can be extremely detrimental to the bird's health. Birds are food items to dogs, and the fact that some dogs are naturally gentle, and that some birds are unnaturally trusting, while making for some wonderful photographic "moments", is not something you can rely upon.
That said, after some weeks or months of being together, though separated, in your home, a very closely supervised one-on-one meeting between one of the dogs and the bird might be attempted. Any show of aggression on either animal's part should be very quickly interrupted and separation again enforced. If the meeting goes well, and they simply look one another over, moving slowly out of simple curiosity, then after a couple of days (to allow the bird to recover from the first meeting), a meeting with the second dog could be arranged under the same circumstances. Be extremely alert for any kind of warning signs, s simple playful snap from the dog could change your bird from a pet to a snack. Over my years of practice, I've been called to attend to injuries resulting from interspecies conflict between dogs, cats and smaller birds and mammals, and the latter don't fare very well as a rule, so if you decide to proceed with this project, be very aware of the potential for disaster. The sites listed by Dr. Salkin will provide useful information as to how to accomplish your objective, but in my experience, the surest approach to peaceful coexistence is not to allow close contact between dogs and much smaller animals. There are exceptions to this rule, but there are also unexpected disastrous incidents that can result in severe injuries and death. If you should have further questions, please let me know.
Kind regards, *****