The pins are there to connect multiple keys to different pad cups on the same hinge rod. In those cases, there is an inner and an outer hinge rod. For example, there are two trill keys that share a single hinge rod but in reality there is an inner hinge inside the outer hinge. This allows the second trill key lever to move the first trill key cup and the first trill key to move the second trill key cup. This means that fewer independent hinge rods are needed. The pins hold the inner key hinge and outer key cup together leaving the outer key hinge and innermost key cup to move independently. To completely disassemble the trill keys requires the pins to be removed. The pins are normally removed only during major flute service. It requires a special tool to remove them. See this video:
"Never give a flute player a screwdriver."
--anonymous--