A word that includes plants and fungi, but not animals
Short Answer 
There is no such word that I can think of.
 Long Answer  
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 &quot;dead ends&quot;
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 &quot;Eukarya&quot;), 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 &quot;kingdoms&quot; 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 &quot;suprakingdoms&quot;) 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 &quot;lump&quot; 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 &quot;flora&quot;
FYI, &quot;flora&quot; has broader usage beyond plants. &quot;flora&quot; can also be used for fungi (e.g., search &quot;fungal flora&quot; on Google). In fact, in microbiology, &quot;flora&quot; (or sometimes &quot;microflora&quot;) 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 &quot;flora&quot; is what you're looking for. I think referring to &quot;all plants and fungi&quot; as &quot;flora&quot; is not clear and will likely not get across the meaning you intend without further annotation/clarification.
Other thoughts:
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 &quot;protists&quot; 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 &quot;multi-cellular sessile organisms&quot; 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 &quot;plants and fungi&quot; :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.