The amateur Freddie Tait had the best round of the afternoon with a 75 while Herd had a disappointing 84 and Kay an even worse 88.
At the end of the day, Taylor led on 155, with Herd on 156, Willie Fernie and David Brown on 157 and Tait on 158.
In the third round, the leading professionals had similar scores but the amateur Tait dropped down the field after an 84.
However he played safely to avoid the bunkers around the green and settled for a five to finish with a 77 and a tie with Taylor.
Taylor finished joint winner of the North Berwick tournament, with Ben Sayers and Willie Fernie, winning £8.