The first thing we need to know is how a Kline line relates to a line in Euclidean Geometry. In the Kline model of hyperbolic geometry, lines are chords of a Euclidean circle.
Make your circle an object by increasing the opacity of the inside of the circle. This can be done by right clicking on the circle, selecting settings, selecting color, and increasing opacity.
Construct two points C and D on the circle, and construct a line through those two points.
Construct the intersection points E and F between the line and the circle. Construct a segment g, between those two points. This segment is your Kline line.
In order to create a tool, click the three bars in the top right corner, then click tools, then create new tool. A box pops up and asks for an output object. The output object you want is your Kline line, which is segment g. Choose segment g from the drop down menu. Then choose input objects. This is what we want the user to select in order to create the line. Choose Point C, Point D and circle c from the drop down menu, and remove Point A and B. Finally click on Name and Icon and rename your tool as "Kline Line."