It has already been done in groovy 
Closed: Is the inability to install flatpaks from Ubuntu/Gnome Software only a temporary limitation?
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Yes, @kenvandine requested the change and the Yaru team came up with a yarufied version of the gnome-software icon. I guess that the package has to be SRUed to Focal first.
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sorry for posting on old post but would a possible solution be to give the user the ability to the flatpak plug-in to the snapped store? i feel like that could be an reasonable compromise. you can add plugins to the deb version, why not add a way to add plugins in the snap version
oops didn’t see iijohnson’s explaination on that; it would at least require a policy in snapd to allow the snap to install flatpaks i suppose
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However, because of the ubiquity of the Flatpak format, and it being the only maintained format for much software, this is logical. I am believing that Snap should win the battle of the formats, but many have disagreed, and thus the Snap store has required the ability to manage Debian files. If it were to gain the ability to manage all of the others, not least Flatpak, its usefulness would be greatly increased.
did you at least read the post by iijohnson? that explains what would needed for the snap store to support managing flatpaks. Someone from the community would have to tackle that as the core team likely have bigger bugs to fry 
also if memory serves if there is a flatpak, there is likely also a snap out there
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I have read the post. Your last assumption is not relevant, because for much software such as KWrite, no Snap version is existent.
i said likely, not guaranteed 
eitherway someone should do for flatpaks what was done for debs as explained in the post i tried to link; once that work is done, it will be easier to argue for flatpak support in the official app store shipped by ubuntu
Hi ,
I’m sorry to post on a “closed” topic .
But it seems to me that if the community wants flatpak support OOTB , the “support flatpak” bug needs more love : https://bugs.launchpad.net/snap-store-desktop/+bug/1950158
Indeed , I think now we all agree that Ubuntu needs flatpak support OOTB , Ubuntu is actually the last distro that does not ( part from arch obviously ) ( You can check here https://www.flatpak.org/setup/ )
On steap that made me think flatpak is important is that SteamOS 3.0 will only allow flatpak for new software ( readonly root partition )