I believe elms in general are "self sterile" they need to be pollinated by a tree of the same species, but of a different clone or cultivar. If you have only one "Chinese elm" for example 'Corticosa' you would need a second elm from a different seed origin, perhaps 'Sejiu' or the normal form 'Lacebark' so that there are unrelated pollen and receptive flowers.
I imagine size is also an issue.
Elm flowers are not very showy. The flowers have no petals, apetalous. Ulmus parvifolia - Chinese elm flowers in early autumn, I believe on current year's growth. Samsaras (seed) develops rapidly and is usually ripe by early winter of the same year, 2 to 3 months. You would need to forego pruning for at least one maybe 2 entire growing seasons to see seed develop. The yellowing and browning leaves can "hide" the browning seed, you might not notice seed if there were only a few.
By the way, one of the key traits in separating one elm species is from another is whether the species flowers in spring, late summer or autumn. And when the seed ripen. These 2 traits are in the diagnostic keys. along with number of teeth on a leaf margin. Very difficult group to correctly identify.