Some won't say
Unsurprisingly, the prominent leaders of prosperity gospel theology rarely if ever address this verse, unlike their opponents. I searched for quite a while and could not find anything on this verse or similar ones from Robert Tilton, Kenneth E. Hagin, or Joel Olsteen*.
* Technically, I did find an interpretation from Joel Olsteen. According to The Babylon Bee, the Joel Olsteen Study Bible explains the meaning of this verse as "Believe in yourself". Then again, the satirical article says that it's the study bible's explanation for every verse.
Prosperity gospel televangelist Creflo Dollar, leader of World Changers Church International, was asked point-blank about this passage in a 2007 interview with CNN. The reporter read Matthew 19:16 and Matthew 19:21-24, then Creflo Dollar gave a response. (I've removed the filler words, since he was speaking off the top of his head).
Well first of all, when the rich, young ruler showed up, and [Jesus] said, "What you need to do is take the things that you have to sell, sell it, and then, come follow me…" It's about loving God with your stuff. If you keep reading down a couple more scriptures, it says "And he received a hundred-fold, everything that he gave, everything that he sold."
So we talk about "is it impossible for rich people to get into heaven?" You know that's not the truth. You know rich people are gonna go to heaven just like average people. The issue there is: will you be willing to take your things and share it with other people. Again, we can't assume just because you have some things, that you automatically are not sharing with the people who need it. We invest in people's lives, not only in our community, but all around the world.
He then goes on to talk about how the prosperity his church preaches about may not necessarily be monetary, but could also be in terms of relationships or other intangibles.
The verse that Dollar refers to with his paraphrase of "he received hundred-fold" appears to be Matthew 19:29, which is indeed a continuation of the passage that was quoted, although it was not directed at the rich man like Dollar implies.
And everyone who has left houses or brothers or sisters or father or mother or wife or children or fields for my sake will receive a hundred times as much and will inherit eternal life.
—New International Version
So according to Dollar, Jesus' words were less about possessing wealth and more about sharing it with others, or in other words, "loving God with your stuff." He also views Jesus' promise of receiving "a hundred times as much" for following him as supporting his argument that Jesus is not speaking against wealth. Furthermore, prosperity does not have to be monetary.
Prosperity gospel author and speaker Kenneth Copeland hasn't said anything on this that I could find, but his wife is quoted in a tweet from their ministry's official Twitter account.
Set your affections on God's Word. Matthew 6:19-20
Refuse to allow your affection to be on
your possessions, business,
treasures and holdings.
Demand that your affections
be set on God's Word.
While this doesn't directly address Matthew 19:24, the verse does begin "Do not store up for yourselves treasures on earth", so I think it has a similar sentiment. The point Gloria makes is that the problem isn't wealth, but rather the affection people have towards that wealth.
I would speculate that Gloria would say the issue of the rich man was not having wealth, but rather his affection towards it. Jesus telling the man to sell his possessions made it clear that he was too attached to his material wealth to focus on God. Thus Jesus' comment about a camel through the eye of a needle was more about the general attachment the rich tend to have towards their possessions, rather than about having wealth.