Vitra soft close sea has stopped working ?

There appears to be three makers who use and supply this unusual type valve.

https://www.google.com/search?q=Vitra+6853-1+replacement+flush+valve

..

any home depot or lowes should have one that will work for you. take the old one with ya

Replace it

You may have to put a weight in the flapper to keep it closed. First try putting pressure in the flapper and let it sit there for a few mnts and check if water still leaking into the bowl, if it does then there could be a crack in the porcelain leaking water or the whole flush valve will need to be replaced. After putting pressure in the flapper and it stops leaking then you just need to put a weight inside the flapper to keep it closed.

You need to replace or clean the 1150464 HINGE KIT http://www.kohlerserviceparts.kohler.com/AccessoriesInformation.aspx?ServicePartID=5563b058e2e042868c7a19398797ecd6

Chances are that the friction washers that control the closure rate are worn out. Most of these are not replaceable so you will need to get a new one. Thanks

No there is no fix, these things rely on friction for the soft close. You will need to replace it.

I trust you mean the "Flapper Valve". They are available and most hardware stores.
Get a Universal type as they fit most units. Take the old one with you. If you turn the water off at the wall it will stop it from running while you're away

the flapper is not closing all the way in the tank. if, when the handle is at rest, the flapper chain is too taut, the flapper is not closing all the way. so loosen the chain. if there is slack, the flapper is not making a good seal and is letting water through. or if in the tank the water is going over the standing up overflow tube, you need to adjust the float. if you have the ball float, lift it up slowly and see if the water stops running. if not, replace the ballcock (valve where the float is attached. if it does stop, unscrew the ball a little or bend the ball arm down a bit until the water stops short of the overflow. if you have the shuttle float, do the same test. if the water does shut off, adjust the shuttle accordingly.