  Global 21-cm experiments are built to study the evolution of the Universe
between the cosmic dawn and the epoch of reionisation. FlexKnot is a function
parameterised by freely moving knots stringed together by splines. Adopting the
FlexKnot function as the signal model has the potential to separate the global
21-cm signal from the foregrounds and systematics while being capable of
recovering the crucial features given by theoretical predictions. In this
paper, we implement the FlexKnot method by integrating twice over a function of
freely moving knots interpolated linearly. The function is also constrained at
the lower frequencies corresponding to the dark ages by theoretical values. The
FlexKnot model is tested in the framework of the realistic data analysis
pipeline of the REACH global signal experiment using simulated antenna
temperature data. We demonstrate that the FlexKnot model performs better than
existing signal models, e.g. the Gaussian signal model, at reconstructing the
shape of the true signals present in the simulated REACH data, especially for
injected signals with complex structures. The capabilities of the FlexKnot
signal model is also tested by introducing various systematics and simulated
global signals of different types. These tests show that four to five knots are
sufficient to recover the general shape of most realistic injected signals,
with or without sinusoidal systematics. We show that true signals whose
absorption trough of amplitude between 120 to 450 mK can be well recovered with
systematics up to about 50 mK.
