Personally, I would never carry multiple annual fee Chase UR cards. I've been out of a game for a couple of years (we moved to Canada two years ago) but I used to just cycle through them -- I'd get a new one, transfer the UR to it, and then downgrade the old one. I always downgrade cards if I have the option, but cancelling them isn't the end of the world. You just don't want to always do that.
I don't know much about the Flex or the Unlimited -- I tend to focus just on sign-up bonuses (e.g. 60000 UR for a $4000 spend in the first 3 months) rather than % cash back. With Chase, you can only get 5 cards every 24 months, though. As long as you're staying within that, I wouldn't say the order is particularly important.
One suggestion I have is to consider business cards as well. I've never had a real side business, but I had a website related to my profession for many years, and I would use that as a business. It never earned money, but I did get invited to be a speaker internationally a few times as a result of it. And I never had trouble getting business credit cards for it (although sometimes I had to speak to customer service).
In the US, one of my favorite travel hacks was to get both a Southwest personal and a Southwest business card, which could easily get you to a Companion Pass. My wife and I alternated doing that every two years, which meant that one of us was almost always free on Southwest.
Chase Ultimate Rewards are great, though. I'm planning to start getting them again, using a US mailing address.