From what I am reading so far about most who resist getting vaccinated and are going against the government’s mandates.
They are mostly using Kuyper’s Sphere Sovereignty in their arguments.

Most say that Kuyper Sphere Sovereignty and One Kingdom Theology are what Kuyper has in mind.
However, others who hold to TKT, say that they actually use Kuyper’s Sphere Sovereignty as a model.
Mainly because God is sovereign over all creation, but He does so in two different ways.
With our governments for example, any power out government’s do have are given by God and we ought
to obey them. Except when it means choosing between obeying God or obeying our government.
With these government mandates, they are forcing many to do just that.

Among TKT however, there seems to be a lot of differences.
For example, many Churches who hold to TKT, such as those in the Gospel Coalition (Canada and the U.S.) believe
the government is within their rights to do what they are doing.

For example, one prominent member of the Gospel Coalition said he believes John MacArthur may have ruined all these years of ministry by his stand against the government.
I of course have no use for the Gospel Coalition.

Concerning Kline, in my reading so far, I have not heard his name come up.