Java code that takes user input of Zipcode and turns it into a bar code
My two cents:

I did not know about this system, so the methods don't tell me much. checkDigit calculates some kind of validation number? Perhaps name it something like calculateCheckDigit. Same for dBarCode.

Also, you only ever call checkDigit on zip once, and then keep on calling it on the checkDigit variable, although this one never changes? Could it be a bug?

Some other comments:


Close the scanner as soon as possible; it is also AutoCloseable, so you can use try-with-resources: try-with-resources
dBarCode can be implemented with a switch statement, an array of Strings or possibly a Map.
I'd extract the zip to barcode functionality of the main method, without the input/output, to a separate function


I think it is fine to leave the functions in one class, and leave them static.