How do I repair my porcelain floor?
The general recommendation for repairing a chip in a porcelain tile is to fill the chip with an epoxy that has as close as color match to the original tile surface as possible. When you go to purchase the epoxy make sure to select a type that indicates that it is suitable for use with porcelain. 

Prepare the chip area for patching by wiping the chipped area and surrounding surface with a microfiber cloth to remove all dust and dirt. Then thoroughly clean the are area with rubbing alcohol to make sure that all oils, remaining dirt and other deposits are completely removed. It is important to let the area full dry after the alcohol wash.

Mix the epoxy according to manufacturer directions on the package. You can use a small discardable container or old clean bottle cap to hold the epoxy while mixing. (Note that if you are working in multiple areas that will take an extended amount of time you may want to prepare the epoxy for only part of the project at a time). 

Use a matchstick or toothpick to apply the epoxy into the chip area a small amount at a time. Work to fill the chipped area level with the surrounding tile surface without overfilling the damaged area. 

Protect the area from traffic or use until the epoxy has completely set up. Some epoxy materials could take till over night to fully harden.