Camera shutter sound wont turn off?

You failed to state where on this planet you live.

In many countries worldwide phone cameras MUST be audible when used or for video display a clear sign such as a flashing light. In those countries phones are sold with the firmware localised to remove the ability to turn off the sound.

The purpose is to prevent invasion of privacy such as candid photography and also to prevent illegal photography in places like law courts and parliamentary buildings or other sensitive locations.

For the record I'm in the UK also using a fully updated iPhone 6 and in silent mode (simply activated using the slider switch located above the volume buttons) the camera is also silent in operation.

You may not have bought it from Japan, but it is still possible that it came from there (based on available info). That's the only explanation I could think of as to why that is the case. Until recently I had an iPhone 6 & the camera shutter went silent with the silent switch enabled.

Replace camera.