Yes and no.
You can have a flexible partial but not a flexible full denture.
Flexible partials are made of a soft, pliable material that conforms to the contours of your mouth, making them more comfortable to wear. They are also less likely to slip or shift when you talk or eat.
At this point in time flexible full dentures do not seem to work well.  If you are having a problem wearing a full upper or lower, you can have a lab made soft liner.