No, you cannot deduct the expenses if you are just writing a book.
When you finally publish and sell the book, you can then deduct expenses if this will be your business. If you report this as a hobby, you cannot deduct the expenses as hobby expenses are not deductible.
You cannot add your child on your tax return to report their business or income. If this is a partnership, then you would only report your portion of the business. Also, since this business would be in the start up phase and not actually "live" yet, you would not be able to deduct the expenses. If this becomes a business, then you would then deduct these expenses as your start up costs.
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