You have a few options. All of them include some amount of coding. There isn't a built in way for SQL Server to export base64 encoded strings as files.
However you can....
Write a CLR that will do it from the TSQL / database side. The relevant C# code you would need in the CLR is something like this:
File.WriteAllBytes(@"c:\yourfile", Convert.FromBase64String(yourBase64String));
This is courtesy of this link: Base64 encoded string to file
Or write a quick console application to run through each of your rows and pull it out. Using the same code snippet above for C# or any other number of languages that are documented out on google. Another method a quick google search found is:
public Image Base64ToImage(string base64String)
{
// Convert Base64 String to byte[]
byte[] imageBytes = Convert.FromBase64String(base64String);
MemoryStream ms = new MemoryStream(imageBytes, 0,
imageBytes.Length);
// Convert byte[] to Image
ms.Write(imageBytes, 0, imageBytes.Length);
Image image = Image.FromStream(ms, true);
return image;
}
Courtesy of here: http://www.dailycoding.com/Posts/convert_image_to_base64_string_and_base64_string_to_image.aspx