Can I use Booksprout if my book is in Kindle Unlimited? (KDP Select)

Since Kindle Unlimited is a specific program, your best source of support would be Amazon directly. 

We recommend keeping your book OUT of Kindle Unlimited for the duration of your review campaign (from when you list it on Booksprout to the review campaign end date). You do not need to delete your book or review campaign from Booksprout once your book is enrolled in Kindle Unlimited. Simply make sure that you have no active campaigns for that book while your book is in Kindle Unlimited.

However here is what we know: technically, it is against the terms of KDP Select to distribute the digital format of your ebook anywhere else other than Amazon, so if your book is enrolled in their program currently, we don't recommend creating a review campaign with us at the same time. It's best to wait until your 90-day period is up and you've unenrolled. That said, some authors choose to make it available anyway and we haven't heard of any problems yet. If you do choose to do it, it will be at your own risk. If Amazon catches you, there could be some repercussions such as not being able to participate in Select anymore.