No. A moss has never borne a flower and never will, because it belongs to a branch of plant life far older than anything that blooms. It multiplies by dust-fine spores rather than by seed, and it manages sex without petals, pollen or a single insect. Several things on a moss do look enough like flowers to keep the question worth asking, so it is worth seeing what they actually are.
Spores where a flower would be
Where a buttercup makes a flower and then a seed, a moss makes a capsule and fills it with spores. Look closely at a moss in season and you will spot them: slender stalks rising from the green cushion, each tipped with a little swollen case, green ripening to brown or fiery red. That stalk and capsule together are a separate generation of the plant, the sporophyte, and it grows out of and depends on the leafy green carpet beneath it. When the spores are ripe the cap falls away and a ring of tiny teeth around the capsule's mouth flexes with the changing humidity, opening in dry air to let the wind carry the spores off. Nothing here is a flower; it is a quite different machine for making the next generation.
Sex without petals
Mosses do reproduce sexually, but they go about it in a way that predates the whole idea of a bloom. Tucked among the leaves at the tips of the shoots sit minute male and female organs, too small to notice without a lens. The male ones release sperm that must swim, through a film of rain or dew, to reach an egg waiting on another shoot. This is why a moss can only complete the cycle when it is genuinely wet, and why so many capsules appear after a spell of damp weather. A flower's apparatus of colour and scent exists to lure pollinators across dry air; a moss, courting in water, had no call for any of it and never developed it.
The "moss flowers" people notice
In spring a mossy bank or wall can flush pink, orange or ruddy brown, as though it were coming into bloom. That colour is a crowd of setae, the fine stalks carrying young capsules, catching the light in their thousands. Bonfire moss throws up a dense forest of them on old fire sites, and redshank moss earns its country name from the reddish setae that stain a heap of them purplish. People quite reasonably read this as a moss in flower; in truth it is a moss in fruit, heavy with spore capsules rather than blossom. The species pages on bonfire moss and redshank moss show the effect at close range.
The mosses that mimic a bloom
A few mosses tease the eye further. On the woodland floor grows rose moss, Rhodobryum roseum, whose leaves open in a broad flat rosette at the top of each stem, so a patch looks strewn with small green flowers; the picture above is a colony of it. The likeness is pure coincidence of shape, since those are ordinary leaves and no petal among them. The haircap mosses play a related trick: the male plants form a neat starry rosette at the shoot tip, a splash cup that catches raindrops and uses the splash to fling sperm to neighbouring plants. It looks for all the world like a tiny tan flower, yet its whole concern is catching and flinging water.
What this means if you grow moss
Because there is no flower there is no seed to buy, and no bag of moss seed on any shelf is what it claims to be. Moss spreads instead from its scattered spores, which need bare, damp, undisturbed ground and a good deal of patience to catch, and far more readily from broken fragments of the living plant, each shard able to root and grow anew; growing moss from spores weighs the slow route against the quick one. That a plant can thrive and spread with no flower at all is one of the quietly surprising things about it, of a piece with having no true roots and no inner plumbing; the companion questions is moss a plant and do mosses have roots fill in the rest of the picture.