I built a mixed aviary last year - mostly parakeets, but also a few finches and button quail. I would be happy to discuss any ideas or questions you have. I am not an expert, by any means, but I do have a little firsthand experience.
This is the thread discussing the build process and introduction of birds:
I began a project recently to convert my old unused greenhouse into a large outdoor aviary for my flock of parakeets. I thought I might share my progress and what I have built so far. This is the greenhouse before I started: It is built off the side of my garage with clear plastic roofing...
forums.avianavenue.com
Speaking of which, I should do an update. It has been a busy couple of months.
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Regarding your second question - introducing new birds to a flock can be challenging. I have raised chickens for many years, starting from just a couple of backyard chickens, up to a flock of thirty plus. This has involved a lot of flock additions, since we didn't have roosters for most of that time.
Interestingly, in my experience, introductions actually tend to get easier as your flock gets bigger. Chickens can be quite aggressive toward new birds - they don't call it "pecking order" for nothing. Whenever birds are added or removed from a flock, the social dynamic changes between the existing birds - some birds move up in the hierarchy. Others move down. Some stay the same. As the group gets bigger and bigger, a few new birds don't upset things quite as much as when you add one new bird to a stable group of two or three birds. Most birds in the flock will take one look at the new birds and know exactly where they stand, so there is no need to fight it out.
Now, if you are doing a mixed finch aviary with docile finch species, they are probably going to give you less trouble than a flock of chickens - despite their reputation for cowardice, chickens can be downright vicious to each other at times. Definitely not docile!
Anyways, there are a couple of things that I feel have helped smooth introductions to my flock. They might not be necessary for your finches, but I think it never hurts to stack the deck in your favor.
First off - it is usually better to introduce all birds into the aviary at the same time, if possible. This is especially true for territorial species, since adding groups at different times means that the early groups will have time to settle in and establish territory before later groups arrive. If your birds are not territorial, this is less of a concern.
With my aviary, I actually decided to release the birds in stages, starting from least likely to cause any problems (button quail) and moving up the most likely (parakeets). I had four groups of birds that were separated from each other during quarantine - one group of finches, one group of quail and two parakeet groups. When it was time to add the birds to the completed aviary, I moved all four groups into the aviary in separate cages at the same time. I let them see and hear each other and acclimate to the aviary environment for a few days while still caged. My original plan was to let the quail get out and explore before introducing the finches, but when I opened the cage ... the quail refused to leave. Rather than forcing the quail out, I opened up the finch cage, to see if they wanted to come out. They did! Eventually the quail took a chance and came out too. It worked out just fine - both of these birds are non-aggressive and they live at different heights. I didn't expect them to cause any trouble and they did not.
I let the finches and quails settle in for a day or so before unleashing the kraken ... I mean, budgie flock. At this point, I had two groups of budgies in separate cages who had very little direct interaction - they were practically strangers, although they had seen and heard each other from a distance.
I was pretty worried about how the parakeet groups would react to each other and the other birds already in the aviary. Budgies can be pretty aggressive toward each other and toward other birds at times, although they are also quite sociable flock birds. I knew there was real potential that something could go wrong, but I was hopeful that it would alright and, if not, I was ready to intervene.
So I crossed my fingers and let 'em loose.
And they were way too busy exploring the aviary and their newfound freedom to bother each other or anyone else. Both groups of budgies merged seamlessly into a single flock of very confused and excited/terrified budgies. The finches and quail were intrigued by the new additions to the aviary. Nobody was aggressive. No pecking or biting. Just a lot of little birds figuring out how to fly in wide open spaces for the first time ever.
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Shortly after that, I was given three re-homed budgies. After quarantining the new birds for several weeks, I needed to introduce the new birds to my established flock in the aviary. This time, I was concerned that the older parakeets might be aggressive or territorial to the new arrivals, so I started off slow, by placing the cage with the new budgies in the safety porch, where they could see and hear my birds, then I moved the cage inside the aviary proper and watched how the birds reacted. They were intrigued. No signs of aggression, just really interested in the cage-o-keets.
I let the new birds acclimate to the sights and sounds of the aviary for another day, then released them. All three parakeets integrated into the existing flock without any issues.
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I honestly don't know if my approach was the best way to do it, but it seemed to work out, thankfully. I think it helps that I was introducing mostly peaceful, flock-loving birds. Lady Gouldian finches and button quail are very peaceful. Budgies can be aggressive at times, but they are also quite social and do well in larger groups. The three bird types largely stick to their own kind and do not bother each other.
It sounds like you have already done research into the finch species that you plan on mixing. As long as the species are compatible and you introduce them together, I think it will be fine. From what I've read and experienced, peaceful finches are a great choice for mixed aviaries. I don't anticipate that you will have too many problems. Just take your time and monitor the birds closely before and after release.