You can use vinegar to clean diamonds but it's not recommended as vinegar can potentially damage the diamond.
While baking soda and vinegar as well as Windex and peroxide does clean diamonds they should not be used on diamonds as they can damage the diamonds overtime.
Safer cleaners for diamonds are mild dish soap and some warm water or even some commercial jewelry cleaners which can help to maintain the brilliance of the diamonds.
If your diamond jewelry contains any porous gemstones such as opals and pearls, you should avoid using vinegar as it can damage them.
Also if you have any delicate or vintage jewelry you should also avoid using vinegar as they are often more fragile and can be more easily damaged with vinegar.
If you clean your diamonds with vinegar occasionally then they likely will not be damaged at least in the short term.
But in the long run the diamonds can eventually be damaged so it's best to avoid use of vinegar for cleaning diamonds.
Mild dish soap and some warm water is the most recommended method of cleaning diamonds at home.
Simply mix a few drops of mild dish soap with some warm water, then soak the diamond jewelry in the warm water and dish soap and then gently scrub the diamond with a soft toothbrush and then rinse and dry the diamond.
And while toothpaste can clean diamonds, it's also not recommended to clean your diamonds with toothpaste as toothpaste contains abrasive particles and chemicals which can scratch and damage the diamond and metal setting of a diamond ring.
It can also dull the diamond's sparkle.