First-Aid Kit for Kitchens
The most important things in cooking first aid kits to me are liquid skin, vitamin C powder, and cortisone cream. Obviously antiseptic and bandages are important too, but I assume those are standard.  

Liquid skin (basically clear nail polish) is antiseptic and helps to seal up cuts so they stop bleeding faster. It also helps to prevent the effect that any kitchen worker will recognize where an otherwise insignificant cut keeps getting reopened and filling your gloves with blood.

The vitamin C powder is a miracle for burns. You put a pinch in some cold water and rinse the burn with it. It's very soothing and seems to help them heal faster.

Cortisone cream is primarily a bakery thing. Prolonged skin exposure to flour frequently causes rashes and cortisone cream helps to relieve the itching and get the rashes to go away faster.