What does the Kenkon stand for?

The 'Kenkon' (Badge/symbol) symbolises Goju Ryu.

'Ken' loosely translates as 'heaven' while 'Kon' loosely translates as 'Earth' thus translating Heaven and Earth.

The round red circle symbolises the vastness of Heaven and the square like symbol in the middle represents the Earth but is also the family symbol of Chojun Miyagi Sensei. (See banner)

'Heaven' represents the Softness of Goju Ryu whilst 'Earth' represents Hard, therefore the essence of the art is Hard and Soft and 'Heaven' and 'Earth'.