There is no such word that I can think of.
Note: although fungi were once considered to be lumped with plants, such classifications fell out of favor 60+ years ago (or sooner). See here for a summary.
Nomenclature "dead ends"
Using the traditional taxonomic approach (including Woese's familiar 3-domain classification system) will not provide the collective term you're looking for. Plants, Animals, and Fungi are all of the kingdoms rank in this system; the only higher rank than kingdom in this system is domain (in this case "Eukarya"), which would include all 3 kingdoms.
If we take a cladistics approach instead, we can investigate Phylogenetic nomenclature. This taxonomic approach lacks categorical ranks such as "kingdoms" and instead tends to use hierarchical group names based on nested ancestral synapomorphies. However, using this approach proves to be even less useful for finding the term you're looking for:
Generally ~6 (5-8) informal supergroups (sometimes called "suprakingdoms") have been recognized based on phylogenetic research. Importantly, 2 of these groups (i.e., clades) are the Opisthokonts (which include fungi and animals) and the Archaeplastids (which include plants). Since animals and fungi share a common ancestor more recently than plants, it's not possible to "lump" plants and fungi together without including animals (and a whole host of other organisms).
You can see a recent publication (Burki et al., 2020) discussing an even more recent proposed organization for classifying Eukaryotes that maintains this phylogenetic distinction and separation between animals/fungi and plants.
Comment on the usage of "flora"
FYI, "flora" has broader usage beyond plants. "flora" can also be used for fungi (e.g., search "fungal flora" on Google). In fact, in microbiology, "flora" (or sometimes "microflora") is used to describe microorganisms in/on a system/host, which would include fungi, bacteria, etc. (For example, see gut flora).
I don't think "flora" is what you're looking for. I think referring to "all plants and fungi" as "flora" is not clear and will likely not get across the meaning you intend without further annotation/clarification.
I momentarily considered if being sessile would be a possible trait to use for delineating these organisms the way you're trying since by definition animals are not sessile (at least not at all stages of their lifecycle). However, many "protists" are also sessile and therefore such delineation would not be exclusive to plants and fungi. Further, I'm not sure all fungi are in fact sessile (though I can't think of any reason why not).
- The phrase "multi-cellular sessile organisms" is probably much more exclusive and encompassing, but probably not 100% perfect. (However, at the point you'd be considering such phrases, I'd just suggest sticking with "plants and fungi" :p).
Perhaps someone else can come up with something, but I couldn't think of any non-outdated ways to accomplish your goal off the top of my head.