If you talk to enough flat-earthers you will discover that two theories dominate the gravity discussion. The first theory is Universal Acceleration which has already been discussed by WTC. The second theory is less developed but claims that gravity does not exist and that objects rise and fall because of density. This density theory is what this post is about.
The first problem with density theory is that is does not actually explain WHY or HOW the density theory works. It only seeks to explain that density exists and therefore removes the need for gravity. The flat earth density theory has yet to explain why density has the ability to move an object.
That being said, there are flaws in the experiments. According to flat-earthers, objects rise and fall ONLY because of density. This is demonstrated by placing various objects in water or showing that a bowling ball falls faster than a feather.
The number 1 issue with the density theory is that is claims that mass does not exist, or that it's irrelevant to why an object rises or falls. This is easily disproved by placing two items of the same density but of differing mass on a scale. One object will go up and the other will go down. But if their density is the same, why don't they both stay at the same height? (Illustration below)
The reason why density experiments work at all is because of gravity. As an object increases in mass, gravity will have a stronger force on it. It can overcome the other forces counteractive gravity. Without a force pulling the object downwards, there is no reason for an object to rise or fall. That force is gravity and it happens that gravity acts stronger on items with mass. It just happens to be true that items with a higher mass often has a high density as well, which is why flat-earthers think density is some explanation. However, in a vacuum all objects fall at the same rate, no matter what the density of the object is.