Sorry for the long delay there - was on vacation the last week!
OK, so there are a few answers here, none of which you're going to love, but the sum total of them will get you where you want to be.
First, when the solution is imported, some defaults need to be set. Specifically, the person doing the solution import is set as the owner of any "record" customizations being created because someone needs to be the owner. This is why the person doing your imports defaults as the owner. There is no way of overriding this default behavior; you can only go back in after the fact and update ownership to change it to something/someone else.
Now, we need to cover some basics from the model-driven app world, which still intersect all these solution components even though you're only surfacing Canvas Apps. In that side of the house, records can be owned by Users or by Teams, and when owned by a Team, it is as though all users who are members of the team had ownership privs (technically there are other kinds of ownership too, but they don't matter for this conversation). PowerAutomate Flows work this way too, so when you look at the Details on a flow and see the Owners, you can Edit this value and assign other owners of the type User or Team.
But wait - you can't find any teams in that list! What gives? Only one team is created for an environment by default; it is the default team for the root business unit, and you can find it by searching on the name of the environment. By default, it will include all users added to this environment. But you want something different: you want your admins to have access and no one else. To do this, you'll need to create a new team. Go to admin.powerplatform.microsoft.com, pick your environment, and go to Settings-->Users + Permissions--> Teams to add a new team (we'll call it "Admins").
Once you create the team, add all the users you want to have ownership for the Flows as Members of the team. With the team created, go back to your flow, find Owners, Edit, and add the team as an owner. Easy Peasy.
But wait--this is a pain! Do I really need to do this for every powerautomate flow I ever make? Thankfully, no. When users leave the system, they might leave tons of pointers in the background; records of all kinds that they own from Business Process Flows to PowerAutomate Flows to actual system records. If that user was an admin, this could be really complex! Luckily, this is a long-solved problem. Way way way back MSFT solved this dilemma by adding a Reassign Records button to the User form. From admin.powerplatform... go to Security--> Users + Permissions--> Users and click Manage Users in Dynamics 365 to open the classic view.
Open the record of the user who has left your org and you will find a ribbon button for Reassign Records. IF YOU HAVE SYSADMIN PRIVS, This will bulk reassign everything everywhere owned by this user to whomever you choose. This is your magic one-stop-shop for disappearing teammates to make sure no records get orphaned.
So by now you're wondering why all this nonsense with Teams and Ownership instead of just granting privs to an app registration. The reason is that Dataverse automatically - and for every record ever retrieved - evaluates the privs of its core security model when determining who can read/write/delete/etc any resource. Sending the flow (or any other record) off to be owned by an app registration is possible, but it wouldn't solve your problem because all the Users you want to manage it still wouldn't be able to see it. For now, you need to play within the confines of the core security model to ensure their visibility, which I think is best done through team membership and ownership.
