How do I move the flashlight app on my iPhone 5S from the control center to the dock (preferred) or home screen (second best)

You can't, as the flashlight is not an app, it's part of the OS. Therefore there is nothing you can move.

Accessing the control centre is completely reliable if you start your upward swipe from below the edge of the screen, alongside the Home button.

David485 wrote:

How do I move the flashlight app on my iPhone 5S from the control center to the dock (preferred) or home screen (second best)

I find that getting to the control center is not reliable because often the iPhone doesn't respond to my swiping up. so I would rather have the flashlight on the dock (4 icons at the bottom), or failing that, on the home screen with the other apps

You cannot.

If you really want it then go to the App Store and download one.

Reply to flashlight is not an app and can't be placed on homepage.... very inconvenient. Is apple planning on fixing this?

I am trying to get an answer to this too. If you find out can you please post. thanks