Turning flowers on the lathe is fairlt easy once you practice it a bit.

Using the proper woods drives the best results. Woods with inconsistent grains, such as Oak, are not good for this.

Since there is already good info available, I will simple list links to the source videos.

The first one is about making small flowers similar to Marigolds or Carnations. Give it a try. Turning Small Flowers Link  

A more involved process is used to create wooden tulips but it is worth the extra time involved.

I have two links you should check out.

Tulips by Carl Jacobson

And

Double Turned Tulips