I use artificial flowers for every holiday and used to just throw them in a large storage container. Then I started washing out my bread bags because they are the perfect length and started saving those little plastic tabs for holding the bag closed.
You can wash and shape the flowers so it does no real harm to squash them slightly getting them into the bag leaving the stems at the opened end of bag and closing them with tabs. The flowers are quite resilient and you usually have to shape them when you use them again anyway. Also you can see what's in the bags and if not just label them. I found this to work for me and is a space saver as well.
This is a page about organizing silk flowers. If you do a lot of crafting using silk flowers, organizing your supply may be a challenge.