I have actually seen some Protestant churches like Assembly of God practicing this Holy Kiss but not very often. It depends on the pastor of the church. There is no rule for practicing Holy Kiss in many Protestant churches whether it should be practiced or not. Some encourage it, some ignore it. An example of encouraging Greeting of any form in Assembly of God.
Greeting is often regulated by cultural acceptance and practices. Today, we embrace/hug, shake hands, pat backs or give high fives. There are not too many practices, even a kiss on the forehead or cheek, that are frowned upon as long as they reflect a genuine and godly spirit. Don’t miss out on opportunities to express your appreciation, thankfulness and love for others. (source)
Greeting each other by kissing is a Jewish custom. They kiss the cheek or mostly on forehead, depends on your relationship with the person but never on the mouth and not between opposite sex. (More information on Jewish Greeting)
In the New Testament also, we see an example of Jewish greeting by kissing, the famous kiss of betrayal called Kiss of Judas.
While he was still speaking a crowd came up, and the man who was called Judas, one of the Twelve, was leading them. He approached Jesus to kiss him, but Jesus asked him, “Judas, are you betraying the Son of Man with a kiss?” (Luke 22:47-48, NIV)