Do all flora possess the capacity to be cloned or viably reproduced from their trimmings, offcuts, and so on?
Or is this trait exclusive to certain varieties; or specific (cultivars) taxa?
The term you need is actually 'vegetatively propagated' rather than 'cloned'. The answer is, essentially, yes, by and large, almost all plants can be vegetatively propagated, though different parts of the plant may be used and the methods used will vary, along with the level of difficulty. Parts which can be used include leaves, stems, shoots, bulbs, rhizomes, stolons, buds and so on.
'Clone' means an exact duplicate of the parent plant, but where plants are chimeric (variegated Sansevieria, for instance) leaf cuttings, whilst they certainly produce new plants, are very unlikely to be variegated, so the cuttings are not clones, though they are vegetatively propagated. Equally, if you took a cutting from a rose and grew it on, it would not be a clone of its parent unless you also took a cutting from the rootstock, grew that on, then grafted the rose cutting onto the cloned rootstock; only then would it actually be a clone.
What varies is the degree of difficulty with vegetative propagation - plants without vascular cambium are harder to propagate, but each variety of plant may need different methods to get success, so if you want to propagate something, it's best to check out the particular plant and its recommended propagation beforehand. More reading on vegetative propagation generally here https://en.m.wikipedia.org/wiki/Vegetative_reproduction