I think the question should be.....are Non-Denominational churches Biblical? As far as I can tell, most non-denominational can only trace their roots to the second half of the 19th century. And even then a lot of these non-denominational have come and gone with more and more sprouting up every day. This don't sound very biblical to me.
Remember, Jesus promised, "I will build my Church and the gates of hell will not prevail against it" (Matt. 16:18). This means that his Church will never be destroyed and will never fall away from him. His Church will survive until his return, it means that the Church will, until the end of time, remain essentially what she is.
What church can make this claim? What Church existed in the tenth century, in the fifth century, and in the first century, faithfully teaching the doctrines given by Christ to the apostles, omitting nothing? What Church can trace it's line of Apostolic succession in unbroken succession, to Peter himself? The Lutheran Church? Nope! The Church of England? Nope! The Mennonite church? Nope! The Presbyterian church? Nope! The Congregational church? Nope! The Methodist church? Nope! The Mormon ("Latter Day Saints") church? Nope! The Seventh Day Adventist church? Nope! I could go on and on and on.
So what Church is it that Jesus promised that the "gates of hell will not prevail against it?" What Church is it that Jesus promised will never be destroyed and will never fall away from him. What Church is it that Jesus promised will survive until his return, and will remain until the end of time, remain essentially what she is? What Church is it that Scripture says is " the church of the living God, the pillar and foundation of truth." The churches I listed above? I think not! I am pretty sure you all know what church Jesus and I am talking about.
Have a Blessed day!