In his attack, Mr Jones pointed out that while Meghan and Harry were "carrying on" about their problems, they were filming "in Africa around the poorest of the poor".
Speaking on 2GB this morning, Alan said: "In the documentary, we’re told Meghan gives a rare glimpse of her new life and struggles as a royal and new a mother,” he said this morning.
"It borders on the insulting. Imagine spending time in Africa where you’re around the poorest of the poor — people who have no possessions — and you’re carrying on about how tough life is.
"Have these two people got no awareness at all?"
"Has she ever wondered whether the poor people in Africa are OK? I’ve seen them, these poor kids with flies on their face and emaciated, with nothing, and the 38-year-old is complaining that people haven’t asked if she was OK," Jones continued.
"She said she’s struggling with duties — what duties? She’s having six weeks off before Christmas for a holiday to LA!"
Mr Jones' comments come after Prince Harry and Meghan Markle announced their desire to move their little family out of the United Kingdom permenantly, due to the negative attention the former actress has been receiving after giving birth to baby Archie.
Prince Harry told his friend, Tom Bradby: "I don’t know where we could live in Africa at the moment.
"We’ve just come from Cape Town, that would be an amazing place for us to be able to base ourselves, of course, it would."
The Duke of Sussex continued: "But with all the problems that are going on there, I just don’t see how we would be able to make as much difference as we want to without the issues and the judgment of how we would be with those surroundings."