DMAIC approach should be used when you don't know the problem and solution but you do have target to achieve.
For example : "We want to reduce our Fossil fuel consumption by 10 %" Here in this project we dont know what are the reasons for high FF consumption but somehow we need to reduce that so first will need to identify problem or reasons for high consumption and then solutions as well, hence we should prefer DMAIC approach.
Kaizen approach should be used where one already knows the problem and the solution
For example: "Changing single drive motor of high HP to multi drive motor of low HP for better performance and low electricity consumption" Here in this case changing motor is itself idea/solution for reducing high electricity consumption.
In a nutshell DMAIC approach to be used for a Goal/problem and Kaizen approach should be used for idea for improvement.