Is is possible to write a decent patent using "only flow charts" to describe a novel method that can be incorporated into larger software systems?
I am assuming that you intend to include a detailed description, and only flow charts as drawings. If this is case, then yes, only flow charts can be included as drawings.
On the other hand, if you intend to include only flow charts, and not a written description, then it will not be acceptable.
Enablement of the proposed invention in the patent specification is one of the important criteria to be fulfilled for the proposed invention to be patentable. The patent specification has to enable a person having ordinary skills in the relevant field of the proposed invention to practice it.
You may want to refer the article at the below link to get insight on different criteria to be satisfied for an invention to be patentable http://www.invntree.com/blogs/how-can-i-find-out-whether-my-invention-patentable
In the U.S. we have something called the "written description requirement", so no. In general the patent application needs to teach "how to make and use" the invention.