Alligator leather, in particular, is one of the most beautiful and durable of the luxurious exotic leathers. Without proper care, the flexibility, durability and overall appearance of alligator leather will diminish drastically. Under normal use and over time, some of the oils that tanners put into the leather will disappear. These oils and compounds must be replaced periodically, in order to maintain the beauty and longevity of your exotic leather product.
NEVER use household chemicals (like Pledge furniture polish), alcohol, or other solvents to clean your exotic leather skins. These harsh products can destroy the natural glazed protein finish on classic alligator finishes, can often remove any coloring or finish applied to skins, and over time leave your bag looking dull and worn. It is also important to understand that you cannot clean exotic skins with polish, oils or creams... you will only seal in the dirt/dust. Your items need to be cleaned first, then conditioned. And, NEVER use nail polish or super glue on your bags!
For matte finishes, use a leather cleaner & conditioner purposed for exotic skins to keep them properly hydrated and providing water and stain resistant qualities. Although Mink Oil can be used successfully on matte finishes only, great care should be taken in its application to avoid stitching as Mink Oil can impact the strength / effectiveness of cotton / cotton blend threads.
Apply a small amount of cleaner / conditioner to the skins, buff off, and then follow with a treatment of the same color polish or cream.
For classes and high gloss bombe finishes, wiping with a soft, clean cotton cloth regularly and a monthly or bi-monthly treatment using a exotic skin specific leather cleaner & conditioner, followed by polishing with the same color polish or cream is recommended.
If your skins are excessively dry, flaky and brittle, this means they have dry-rotted (which happens when natural oils are not replaced into the skins over a long period of time, or they have been exposed to moisture / water). Unfortunately, and sadly, the item is probably beyond rehydration, and your best bet is to retire it.