TL;DR: We don't know.
Wikipedia says that the voice actor's identity is unknown, but cites the interview you quoted, which doesn't say anything about who that actor was or whether their identity is known:
According to a 2012 interview in Maxim, Sam J. Jones had disagreements of some sort with De Laurentiis and departed prior to post-production, which resulted in a substantial proportion of his dialogue being dubbed by a professional voice actor, whose identity is still a mystery.
Director Mike Hodges said:
I was very fond of Sam but here's what happened: we did the main shooting up until Christmas and then we stopped for the break. After Christmas I came back and did all of the second unit stuff too. For instance, I had to do the shots with the flying men and that sort of thing—what passed as special effects back then (laughs). So I also had to shoot a whole bunch of other stuff with a stunt double for Sam and I had to re-voice the occasional line of dialogue too. Not much but some—and I got somebody to impersonate Sam's voice. You would never know it wasn't him.
But Sam found out and I think that was one factor that led to him being upset. And Dino and he just did not see eye to eye for a while. So when you lose your main star there can't really be a sequel.
An article in Empire Magazine doesn't help much (emphasis mine):
Director Mike Hodges keeps the pace cracking and shoots the whole piece from the crazy angles and in the lush colours of the original comic books. Queen's rock operatics deliver a score which is almost unique in being utterly inseparable from the success of the movie and Jones, now residing in DTV hell, deports himself admirably as the golden space boy - even if 80 per cent of his lines are dubbed by a still undisclosed voice.
Nor does TV Tropes, which also confirms the fact that the voice actor is unidentified:
On Flash Gordon, Sam J. Jones' voice was overdubbed by an uncredited actor whose identity remains a mystery to this day after Jones refused to return for post-production.