There are around 25,000 different species of orchid and they're not all the same! Click on 'Propagation' here, to learn about which ones form plantlets:
https://www.rhs.org.uk/advice/profile?pid=333
If you really do mean 'flowers' though, any orchid should continue producing flowers if it's cared for properly.
Yes! Don’t throw it away. Keep it in a semi shade window, water infrequently, and next spring ( or maybe before) you will see new stems growing and lovely big buds.
If it's the type you see in supermarkets and other shops that sell house plants, it will bloom several times a year. Mine does...in fact it is now...with previous blooms having only just shriveled up. It seems to need very little water...only a bit every few weeks now, more in summer.
Mine sits in a West window behind a sheer curtain.
My orchids flowered more than once, although one never did.
However, it produced a baby orchid - which I left attached to the parent plant, only splitting it off last year. The parent plant has now produced another baby - its still attached and I'm not sure which has produced the growing flower stalk! Both these babies have come from the base of the plant.
Another orchid produced 2 babies (at the same time) on the flower stalk. I eventually potted them after a couple of years when the started growing roots.
Remember when repotting orchids the roots like to see light - hence why the pots are clear.