The "Fernandez" theory was floated by William M. Doerflinger in the early 1951.

Two years later folklorist Horace Beck cast extreme doubt on the theory, saying that the correspondenc es (for example, caring parents, piracy, Cuba, repentance, temperance message, "Dead men tell no tales") are generic and virtually inevitable for the time and topic.

On the other hand, Fernandez explicitly says "I am a Spaniard," whereas Hollohan/ Hollander/Anderson in the song is just as explicitly Irish. Fernandez serves no apprenticeship, his downfall begins not in Bermuda but New Orleans. There's no "Captain Moore" or "Flying Cloud," no slaving voyage, no British man-o'-war.

So I agree with Beck. (However, I and William of Ockham disagree with his thesis that "FC" is a conflation of two entirely hypothetical "lost ballads.")
It may be that the author of "The Flying Cloud" read Fernandez's confession at some point. It is more likely, perhaps, that he didn't. And he probably read other stories of piracy as well.

So the influence of Fernandez on "FC" was probably slim to none.

Read the entire "Dying Declaration" and judge for yourself:

https://tinyurl.com/yam4pb5k