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
With effort, any plant can be cloned (i.e. propagated vegetatively), but some species do it more readily and more naturally than others. Not all can be propagated this way "naturally".
The plants that are easiest to propagate vegetatively are those that root readily from a shoot, and those that spread by rhizomes or dividing bulbs, or that naturally propagate vegetatively such as by aboveground bulblets, aboveground stems that root, or other means. In this case, you can just take the new plant generated.
Some plants do not tend to propagate vegetatively on their own, but can be induced to do so without much trouble, such as by taking a stem cutting, or layering them (burying a stem under soil until it grows roots.)
An even broader range of plants will not root if layered or if cuttings are taken, but can be induced to do so by the application of the right type of rooting hormone. By this method, the rooting of most trees and shrubs is possible, as well as many herbaceous plants.
The best methods for propagating a particular plant can vary a lot by the species, sometimes even for closely-related species. In general though, certain restrictions and commonalities in method tend to apply to broad groupings. If you want to propagate a particular plant, it is best to research methods for the specific species.