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)
Holy Kiss was indeed encouraged by the Apostles, who happened to be Jews, but it is not clear whether this Jewish custom should be continued by Christians or not. The most important message the Apostles left us is that Christians should love each other and greet whenever we meet.
Whether or not the holy kiss should be a tradition we carry on today is not clear in Scripture. Whether or not our salutations to our brothers and sisters in Christ include the holy kiss, the important thing is that our greetings spring from real love and friendship, be characterized by sincerity, and represent true Christian fellowship. (source)