No, each ring was linked specifically to each user. They were unable to switch rings or control each other elemental aspects. Nor were there any episodes where ring switching ever took place (however rings were stolen from the heroes several times over the run of the series.)
The very premise sets up the show indicating each hero was aligned with a particular element and mindset. Each was linked with their ring and their power was unavailable to anyone else.
From the introduction to the show:
"Our world is in peril. Gaia, the spirit of the Earth, can no longer withstand the destruction plaguing our planet. She sends five rings to five special young people:
- Kwame, from Africa, with the power of Earth...
- From North America, Wheeler, with the power of Fire...
- From The Soviet Union , Linka, with the power of Wind.
- From Asia, Gi, with the power of Water...
- and from South America, Ma-Ti with the power of Heart.
- With the five powers combined they summon Earth's greatest champion, Captain Planet."
Each Planeteer was linked to their element by their temperament and as strange as it sounds if one of them was to be absent or removed from the Time stream as when Wheeler refuses the call from Gaia in the episodes "Two Futures, Part One and Part Two" it caused an entire collapse of the story universe as if there was no other person who could have taken Wheeler's place as the wielder of the Ring of Fire.
- I consider it a morality tale seeing how Gaia claims that this group are the "first Planeteers", but in later episodes, such as Hog Tide, she tells the Planeteers stories of earlier generations having served the Earth in the same way, with the same powers.
Gaia indicates that without Wheeler's intervention, the rest of the Planeteer's did not continue and stopped working together. Granted this smacks of a morality tale where Gaia gives Wheeler the option of going back through time and correcting his mistake but it certainly appeared there was no one else who could use the Ring of Fire in his absence.
This was a children's show aimed at a very young demographic. Most of its themes were light-hearted and in keeping with cartoons of the period. It produced 6 seasons and over one hundred episodes. As such:
The show was kept very simple, with simple themes, simple ideas and very comic villains. Each hero was strongly associated with their ring, so the idea of switching them was probably never going to happen often, if at all.
The ring wielders NEVER used the full range of abilities capable in their rings. If they did, Captain Planet would never have to be summoned. Only in one episode did Ma-Ti use his mind control powers to the fullest extent to dominate and control people with it (Two Futures, Part One and Part Two).
I suspect part of the show's guidelines included keeping the rings under-performing so Captain Planet could make his appearance and give his sermon about protecting the environment.