So, I have the kitchen composter (on this site its just a green plastic one with a carbon filter) and I mostly compost kitchen scraps, shredded paper and flowers that die in my house. How long should I reasonably wait til it gets started? What could I possibly be doing wrong?

http://www.planetnatural.com/site/compost-container.html

You can start a pile whenever you want, no special time or amount. If you generate small amounts of stuff and don't have a pile started, just dig a hole in a flower bed, in the well of a tree, or around some other existing vegetation... put in your compost material, fill hole with water to the top, and cover with the soil you dug for the hole! Nothing fancy, but you have compost started and going to work. Depending on where you live, your moisture/rainfall/etc., water frequently to keep the buried material decomposing... Your existing vegetation will love you!