part and part of is used more and more for code generation scenarios recently (instead of deprecated transformers) and unlikely to go away anytime soon.
Packages like built_value, json_serializable, and many others depend on it.
Discouraged is only the patter where all files of a package are tied together to a single library by having one library file and all other files being part of that library.
original
In Dart, private members are accessible within the same library. With import you import a library and can access only its public members. With part/part of you can split one library into several files and private members are accessible for all code within these files.
see clarifications to below paragraph in above update
Using part / part of is discouraged and the Dart team is considering getting rid of it. I assume they will introduce something like "friend" (https: