Where should I put my dart files if they are the server side files of restful api providers?
You can create an src within lib and put your files there.
If the files are executable, you can put them inside bin, or within a directory inside bin.
See the package layout conventions for details.
Many applications use third-party software.
Third-party software often organized as pluggable functionality.
Pluggable functionality often implemented not as independent executables but as linked libraries.
Also when you wrote application then you often divide it on different functionality.
The best way in this case (in Dart) put different functionality in different libraries.This simplify your life when you will be testing and maintain your application.
By convention libraries in Dart resides in 'lib' directory.Also implementation of libraries by convention must be located in 'lib/src' directory.
There may also be other possible explanations for this need.I just tried explain it to you as simple as possible.