It's probably safe to assume Saint Blaise
is enjoying Paradise these days.
Martyrdom likely led him to eternal glory
and not just some fish story.
Now Chesterton has appeared in segments of the in the EWTN series G. K. Chesterton: The Apostle of Common Sense. And, of course, his character Father Brown has been the subject of at least two movies (Father Brown. Detective and The Detective) and two television series (the first in 1974 and a current one that began in 2013 and is still being produced). I've even heard of movies based on Magic and The Man Who Was Thursday, though I have seen neither.
But no biographical movies.
There's potential, certainly. His discovery of faith and his later conversion to Catholicism, his encounter with the diabolist, his courtship of Frances, the debates with Shaw, the Marconi scandal, and so on.
But no biopics.
I can think of a few possible reasons.
His books are not as popular or as widely known as those of Tolkien or Lewis. His audience tends to be more limited, and for a long time his reputation had waned or was obscured.
His writing style, while popular in his day, is sometimes a challenge for modern readers, hence he is less read than Tolkien and Lewis. Father Brown is his most popular character, but the two Father Brown television shows were shown in the U.S. on PBS, which tends to draw a small audience. .
Chesterton died in the 1930's while Lewis lived until the 1960's and Tolkien to the 1970's, so he is a more distant figure.
There have been accusations of anti-Semitism, which, while supporters have argued persuasively against them, still linger. Certainly those accusations have interfered with his cause for canonization. One suspects the possibility of controversy has made movie makers hesitant.
And, to be honest, he was not photogenic, especially later in life when he was very heavy and dressed in eccentric ways. Even as a young man before he gained weight he was not exactly a looker. (I say this as one who always described himself as having a face made for radio!)