What is the relationship between an FDD and a DFD of the same system?
Functional decomposition is about partitioning the functionality of a big complicated system, into smaller, preferably simpler parts. The FDD is a tool that aids you in this process. Basically, you are breaking down of the capabilities of a complicated system, into a set of more specific logically grouped capabilities.
Now, a data flow diagram deals with how data flows through a system for a specific function of the system. So, each of the above mentioned capabilities might very well have their own unique data flows.
For example, if you have an FDD diagram describing a blogging system. You might have functions for say, displaying a blog post, editing a blog post and potentially sending a link to a blog post to a friend.
These three functions will all have fairly different data flows, which can be modelled separately with DFDs. So, I'd say the relationship between these two types of diagrams are that one can help identify the individual functions, which might, or might not, need to have an associated dataflow mapped.
Hope that is helpful.