Since your diary does not say what type of plant this is, giving an answer can only be general in nature. (where have I heard that before?)
If it is an auto flower, you will not have to change a thing, it will start flowering no matter what lighting schedule you are using.
If it is a photo period plant, you will need to switch to 12/12 to initiate flowering. This is best done when your plant either fills the grow area horizontally, like in a SCROG set up or when your plants reach about one third to half the available height for vertical growth.
Although your grow chamber is rather impressive, a certain amount of light will be "lost" due to having to pass through the glass (reflection & refraction) and having the lights in direct contact with the glass, can cause heat issues for your lights and may diminish their effectiveness prematurely.
After seeing the height of your DWC bucket, you vertical space is a bit limited, so I would concentrate on further LST until your space is more or less filled in horizontally, before switching to 12/12, if indeed it is a photo period plant, which may take another 1-4 weeks, depending ,obviously, on how fast your plant grows.
If it is an auto flower, the plant will begin flowering when she is ready, regardless of what you do.
Hope this helps,...... Organoman.