Basically a Witch's Book of Shadows is a place where they keep Prayers, Spells, Devotion, Altar Diagrams, Information on the Sabbats, Important dates (Birthdays, Handfastings, Deaths), Information on thier God & Goddess, Herbs, and their craft. A book of shadows is a very personal thing,and should contain the information you find most important.
So after you get to know what a book of shadows basically is, you can tell yourself if you are able to use it or not.
Indeed, a satanist or any person who wants to keep their spells, rituals, prayers, devotion, altar diagrams, important dates or any other sort of magic information, can start using a magick book of shadows.
Perhaps you asked about it since you do not know if a statanists can be witches. The answer is yes. You probably think that witchcraft is associated only with wicca and paganism, which is not ture and a huge misconception. A witch is anyone who casts spells. Even Satanists and Christians could be considered witches if they cast spells and do magic, but they aren't Wiccan because they follow a different religion than Wiccans. A Wiccan is someone who follows the religion of Wicca, which is an officially recognized religion just like Christianity, Judaism, Islam, and Buddhism. If you get nothing else from this, remember that "Wicca" is the name of the religion and "Wiccans" are the followers of Wicca. So feel free to do whatever you will, make a book of shadows if you wish or any other magical thing.
But, from your post I can assume that you are also asking if it is necessary since you asked if you "need" it.
You have to remember that most things in magick are only optional, and none of them is necesary or needed. Book of shadows is in that "not necessary" list.
Witches basically choose if to make their magick book of shadows but nobody says that it must be necessarily done. You have to follow your free will, but remember that nothing is necessary and that a witch can be practicing the craft without making a book of shadows as well. But I do recommend making your own book of shadows, but I had to point out that you do not need to do it in order to practice witchcraft.
Do you wish to make a magick book of shadows? Go for it.
Do you wish not to make a magick book of shadows and practice the craft? Do what you will and go for it.