I would avoid disturbing the soil within 2 feet of the trunk, and not dig any deeper than 6 inches beyond that. Flowers that are easy to grow from seed, such as dwarf Nasturtiums, Violas, or Calendulas may be an answer, too.

Welcome to GoY
I agree do not dig too deep nor to close to the stems.
if it is shady think of the small bedding begonias.
if it gets sun then most annual bedding plants would be ok. Bedding verbena, petunias, salvia, nemesia etc Just remember that they will need plenty of water as the cordyline will also need it too.

Thanks for your help I will look for the variety’s of bedding plant you have both suggested