When did people start using flowers as decorations? Was it just wealthy people?

Not exactly "decoration" in the sense of decorating your home, but a Neanderthal skeleton from Shanidar Cave in Iraq has evidence of being buried with flowers. Subsequent analysis suggests that the flowers were probably brought into the grave after the burial by burrowing rodents, but it at least raises the possibility that people were using flowers in a decorative way from even before we were modern humans.

On the other hand, we also have evidence of flower designs on items such as pottery in a lot of places around the world from fairly early on. They aren't actual flowers, but the idea of flowers (or representations of flowers) being decorative is fairly old. That said, it is going to differ a lot from area to area. For instance, in the U.S. Southwest you don't actually get many flower designs on pottery until fairly recently (ca. A.D.1300), but this is probably mostly because pottery designs were almost entirely geometric before this point, and representation designs (including flowers, such as sunflowers) only appeared after about A.D.1300. You do get earlier examples of flowers, such as the carved and painted wooden flowers from Pueblo Bonito in Chaco Canyon (ca. A.D.1100), but these are both rare and probably used for ritual and not purely decoration.

Of course, that brings up another issue of where decoration intersects with ritual and how to separate the two, but that seems a bit tangential to your question so I won't get into it. Suffice to say there is a very old complex of imagery and religious beliefs in the U.S. Southwest (and in Mesoamerica) known as the "flower world" which associates flowers (and colorful birds and insects) with the upper world (or "heaven" to use a very inappropriate analogy). Flowers are most likely not considered purely decorative in this tradition and have other social significance. Consider white roses at a wedding as opposed to any other kind of flower or color of rose. They are certainly decorative, but they are also symbolic and have particular social functions beyond just being decorative.