Lets be honest, Mink OIl is really a boot treatment, but I use it for knife sheaths and bushcraft kit that is subject to hard wear. It is also great on hard used motorcycle leathers. It significantly adds to water resistance and, because it has a 'thick' consistency it helps to seal stitch holes.
The downsides: Mink oil will almost certainly darken your leather slightly. It is an oil based product and will soak in quickly but it tends to sit on the surface to protect the leather. It is not a shiny finish. You can buff and polish for hours but it ain't going to give you a parade ground gloss.
Apply with a sponge or cloth, lots of light coats are better than one heavy one.
You might want to try warming the item with a hair dryer (not too hot please!) to help the oil melt into the leather's fibres.
Have fun but remember this is an oil based product and don't get it anywhere it doesn't belong...
If in doubt, try on a small corner before 'splashing it all over'.