You're asking a few different questions which I'll try to answer.
Here is an article I wrote that might help your understanding of FlashBASIC. In short, where traditional MV BASIC is compiled and then run by assembler, the Flash compiler is C and generates an object module that sits below the standard BASIC object in frame space. At runtime that code is then interpreted by a C runtime. For our purposes here, there is no C interface, this is just an internal mechanism for getting code to run faster.
Note from the above that this is Not related to the "What's an object file in C?" topic because object modules in D3 are stored in D3 frames, completely unrelated to common OS-level object modules.
Now about C calling Pick - in your case D3: You can use the CP library - the docs are in the same area as the link you cited. Rather than binding with the database itself, you can also use your code in a client/server mode with the MVSP library if you're using Managed C (.NET). Or you can use any common web service client mechanism in C and setup D3 as a web service server with a number of technologies including MVST, mv.NET, Java, or C/C++.
I know that response is rather vague but you're asking a question which has been discussed at-length in forums over a period of years. If you ask a more specific question you'll get a specific answer. Feel free to refine your query in a comment and we can focus the answer.
Also note that you tagged this question as "u2". If you are really using the U2 variant of MV/Pick (Universe or Unidata) then the reference to the D3 docs was misleading and none of the above applies, as they do this differently in U2 and there is no FlashBASIC there. I know, you're confused. Let's work it out...