It isn't a Nook Kids App, but just the regular Nook App that you can get for free in the Google Play store, so the "Nook Kids" books, Read to Me books including Kitereaders, are NOT available on the Samsung Kids Tablet. There is no Nook Kids App for Android.
Today Barnes and Noble announced that Samsung would Pre-Load B&N Nook App on Galaxy Tab 3 Kids. This means all the Nook Kids eBooks (~6700 titles) currently available on Barnes & Noble (refer to http://bit.ly/NK-BestSellers) will be on also now available on Samsung Galaxy Tab 3 for Kids for purchase. This is a second distribution announcement from Barnes and Noble’s Nook Kids division this year – in June 2013 they did a similar deal with Fuhu’s popular Nabi tablet for kids.
Since KiteReaders has a strategic distribution relationship with BN Nook Media – all the titles distributed by KR on Nook Kids will be now also available on Samsung’s new kids tablet via this deal.