Angels are a single or 4+ group kind of fish. Many people have kept them solo and many people who have tried to keep them solo are disappointed in their personalities. I personally believe angels personalities shine far brighter in groups of four or more, but they can be kept solo with no health issues as a result.
Having said that, I am growing out about 20 1-1.5" Philly blue angels in a 55 all their own. I am going to pick my four favorites and add them to my 125 and pick another 6 and keep them in the 55 with a group of 8 sterbai cories.
I would also remove the idea of the bichirs unless you intend to move them to a larger home. The species of bichir you are talking about can grow to 18" and will be very cramped in that 55. Two of them would take up a massive amount of space on the bottom.
There is nothing wrong with housing bichirs and angels together. It is highly unlikely they will interact at all, much less have aggression issues. So if you want to upgrade the tank to at least a 90 for one bichir or a 125 for two bichirs, you could house the rainbows and some angels. A 90 would hold about 4 of each while a 125 would hold 6 of each.
Now if you don't plan on an upgrade, I would pass on the bichirs. Their size is just too much for that tank and they add a very large amount of waste to the bioload. Instead, I would plan for a school of 8-12 Cory catfish with 4 angels and some schooling tetras of a medium body (like lemon tetras, bleeding hearts, black skirts, etc).
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Thank you for the very detailed answer. I've read angles either do best solo or in groups of 4-6 or more. I'm still debating on weather or not I want one. I has kind of moved passed them but saw a beautiful solid black angle at a LFS that rekendiled my interest in them. Still going to debate as I'm not going to rus into one lol. I really like them and all but still balancing out my stock.
I actually already have one small Senegal bichir and decided to stick with just one instead of two. He/she is about 3.5-4 inches right now. I do plan on upgrading as he grows out, the bigger the tank the better! So far stock plans include the bichir and with 4 rainbow cichlids.