Hi and welcome
Can you give us a little more info please? Is someone sitting in the chair and rocking it?
If the bottom of the rockers are flat, how about buying some of the non-slip stuff that goes under carpets on solid wood floors to stop them slipping.
Here is a link. Wal Mart sells something like this for a lot less. http://www.addarug.com/DisplayLargeImage.cfm?ParentID=138&ItemTitleWeb=Rug-Preserver-Organic&Category=139
Cut it into a narrow strips and glue it to the bottom of the rockers with Elmer's Glue.
I have also been reminded by a fellow expert (thanks Smithy) that if the rockers are loose, or ill fitting then they will move slightly when rocking. This will cause the 'walking' you refer to.
Check to see if the rockers are firmly fixed.
Most of the products you'll find, as above, are floor and carpet protectors. I have found most of those products to not help in preventing a rocking chair from moving across the floor. I have an antique fold up rocker. It use to do the same thing.. You need a product that will suction the floor, not damage the floor and have some means of stability.
With a bit of creativity I decided to use, what we call in my industry, bumpkins. You may be aware of these if you look behind any wall art you may have in your home. They are basically protectors placed on the back of an art piece to prevent wall damage. They are small , round, clear rubber self adhesive "dots" Don't use cork that you may see on your artwork, it will not prevent movement
You can purchase these at any Craft or art supply store. Place one "bumpkin" at the tip, the center and the rear tip of the rocker feet platforms. Then again about 1/2 of the way between each of the first placed bumpkins. If your rocker is older you may have to adjust both sides so that the rockers sits evenly. The bumpkins can be easily removed if you need to readjust and you can add as many as needed. This should solve your rocker walking issue.
Best of luck!