I'm taking a look at the following books:
Sight Reading & Rhythm Every Day
Improve Your Sight Reading - Paul Harris
I just want advice whether it is necessary to do books 1 and 2. I want to skip to book 3 (I feel like level 3 sightreader)
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I guess it depends on what you mean by 'I feel like a level 3 sightreader'.
If you have a teacher, they would be a good person to ask; part of their job is to assess where you are at, and what will be most helpful for your musical development.
But I'm guessing that you probably don't have one? That's fine; you just need to do that self assessment thing yourself.
Now, I don't know you, and I don't know those particular books, but to get an answer, I would ask:
If the answer to either of those is no, then I'd consider Book 2. You don't want to start too advanced and then get frustrated. If you're comfortable, you might as well get Book 3, and give it a go. If it's too hard, do Book 2, then come back to Book 3 later.
If someone is familiar with this specific series, I'm sure they'll be able to give you a more specific answer.