I don't understand several of your terms and therefore do not understand what you did.
21 footages and a header.
What is "a header"? Is this something you added, or just the first part of the dvd structure?
individual VOB file.
Encore builds your project into multiple vob files unless it is very short. I'm not sure what you are referring to as a single vob file.
I created 22 timelines and put them like a straight line in the Encore flowchart.
I assume that the end action of timeline 1 is timeline 2. And the end action of timeline 2 is timeline 3, etc. Is that right?
You might post a screenshot of your flowchart.
When I played the DVD on any player, it will just play like what I did on Encore, the order was right from 1 to 21.
You describe your initial tests as playing on different computers. What happens on a DVD player attached to a TV?
By the DVD standard, a VOB (Video Object) can only be ~ 1GB in size. If one's Timeline Duration and Bit-Rate exceed that ~ 1GB size, then Encore will span to as many VOB's, as is required.
You will need to do bit-budgeting, to determine the Bit-Rate for the Transcoding of your set Duration, to make sure that it fits within the ~ 1GB VOB size.
Why does the client need a single VOB? That is an odd request, but there might well be a real reason for the request.