When Seth came for the first time, he delivered the only copy to Claire. Later, Stamper grabbed the book and made their moves to achieve what he needed. Now, regarding Seth's possibilities of having a copy, I don't think (my opinion) Seth has a copy because it will be a risky move against Underwood. Besides, Seth admire in some way to Underwood. I'm going to refer two strategic scenes to answer more deeply the question. First, Seth prefered to be WITH Frank and not against.
Remember this conversation:
- Frank: Are there any copy of the journal?
- Seth: No, I gave Mrs. Underwood the original and told her to check.
- F: Did you give him (referring to Remy) anything else?
- S: I got anything else. And even if I had it, I wouldn't.
And then, later in the same conversation, he asked why he changed of band and delivered probably a nuclear bomb that would destroy Claire and Frank.
At this moment, is valid to remember that Claire's recommendation was to keep under observation to Seth and Douglas did it.
- Seth: You're the Vice-President of the United States, Remy works for Raymond Tusk.That puts me in the middle of two important people. I had to be careful.
- Frank: I'm sure Remy is offering you lots of money.
- Seth: When I saw you taking the Congress in the Social Reform, I realized where the real power is. I want to work for you, not navigate in a yacht. Money doesn't interest me.
With that in mind, only both Underwood and Douglas had access to that document. Douglas then, burned the only copy of that journal. So, in conclusion Seth wouldn't earned anything making a copy of that journal and no, he doesn't have a copy.