You would use the block pos you would get to get the tile entity at that pos, check if it’s yours & get the data from it.
However, with the ID limit expansion in 1.13 I would just use seperate blocks (not seperate classes) for each colour the way shulker boxes do it (with an enum). Meta is great for facing, but you shouldnt be using a TE for something like this as you can avoid all the overhead of it by just using multiple blocks