1. As DD passed 11+ is there any point in providing additional academic evidence or is this sufficient in itself?
Assuming that WOK is a flat pass mark, no, you don't need to provide further academic evidence. Your appeal is purely against oversubscription.
2. Could the fact that DD is currently at a private school count against us?
Neither Etienne nor I have ever believed that this is an issue at appeals. Admittedly, we hail from Bucks where there is a definite pattern of children attending prep schools in the hope of accessing the grammar system more readily at 11+, but I doubt Kent is very different from that.
3. Would it be useful to produce an Ed Psych report as evidence ? It specifically states that she would do well against a grammar school.
No - as above. Your appeal is against O/S. However, if the EP report suggests the existence of SEN in any form, and WOK could be the best school to help her deal with those issues, that would be very pertinent indeed.