FE "explains" it with celestial gravitation. AKA everything but the Earth has gravity. http://wiki.tfes.org/Celestial_Gravitation
It doesn't really explain it. Gravity varies between equator and poles - which isn't easily explained by celestial gravitation. But it also varies (slightly) according to what rocks are below the surface - at the tops of mountains, etc.
Honestly, if I were a flat earther, I'd go with "standard gravity" - make the world infinite in horizontal extent and finite thickness...with the thickness getting slightly less under the equator...maybe god put a massive aluminium support girder under there?
Trouble with these ideas are that they can't reproduce tides correctly.
FE'ers claim that the moon DOES have gravity - which might produce tides...but it wouldn't explain why we get TWO high and TWO low tides each day when the moon only moves overhead just once.
Still waiting on a good answer for that one!