Scotland voted overwhelmingly to remain in the European Union, while the majority of United Kingdom residents voted to leave. Therefore, many Scottish residents are upset that they will no longer be a part of the European Union. Furthermore, many Scottish residents already felt a wedge between themselves and the rest of Great Britain. In short, the U.K. referendum vote will likely have significant bearing on the issue of Scotland's independence.
J.K. Rowling believes Scotland will seek independence, Brexit will have a strong bearing on Scotland's future decisions. Scotland had voted strongly to stay in the EU, Scotland's First Minister and SNP leader Nicola Sturgeon also holds the view like J. K. Rowling that Brexit would have an impact on how the people of Scotland would connect this decision with Scotland's independence.
However, everyone needs to recognise that Scotland should be allowed to make this decision themselves and if they are able to realise even half of the ambitious plans they have for the country then they have a chance to build a better country.
As the author rightly points out, the extremists on both sides have engaged in a terrible amount of abuse and disinformation but hopefully, voters will be able to see through that.
An author of children's books does not have influence over such an important decision. Scotland wanted to stay in the EU and if permitted probably will vote for independence, but not because of her. There are a huge number of reasons for Scotland to become independent, wizards are not one of them.