Am I able to make a bunch of gumpaste flowers and store them for a later time?

of course, just put them in a air tight container and keep them out of direct sun light.

Just make sure they are very very dry before you put them in the air tight container or the moisture will make them soft again.

What recommendations can be made to keep the container dry in humid areas? Rice? Silica? Limestone? anything at all that helps keep the container dry as dry can be?

How long can I make them in advance?

Geraldine Randsome carries a food product that is meant for humidity and condensation. Its called Decassant or something like that. It looks like the stuff you get in the bags from the hardware store for your closets called Damp Rid. Im sure you can use Damp Rid too because its in a bag and doesnt come in contact with the flowers. But I know the Decassant does work. Especially for cakes coming out of the fridge and condensation on them. Her site is creative cutters.

rice will work?

Probably but the only thing I worry about with rice is weevels. I know my mom used to get them in the summer and she didnt have air conditioning. Not sure if the two are connected but I certainly wouldnt want bugs on my roses!!

It's fairly humid here and I have no trouble storing gumpaste flowers. I've got some stored in a loosely tied plastic bag (it's a basket bag put over the arrangement) and some others stored inside a styrofoam ice chest and they're all doing fine. I've also stored fondant flowers in a cardboard box lined with paper towels and they've kept for months that way.

In my experience, you will usually need a dessicant like silica gel if using an airtight box.