How to get flavours to infuse into rice
Nasi lemak means fat rice. The fat is from the coconut milk, which is up to 20% fat depending on how you make it. The fat will change the flavour and mouth feel of the rice but it is not particularly going to give a strong flavour .
The nasi lemak needs aromatics in the rice. These would be lemongrass, ginger and pandan leaf. Pandan leaf is particularly important. The lemongrass and pandan are whole and don't disappear in cooking so will continue to impart aroma to the surrounding rice even after it is cooked.
Nasi lemak is mainly about the condiments so the rice is not supposed to be too strong since you have fried fish, sambal, etc. But with the herbs you will get a good aroma in the rice.
You could also try adding shallots lightly fried before cooking (in addition to the aromatics)
Rice is not really boiled but steamed in SE Asian cooking. Just use a rice cooker. The other ingredients are optional, but coconut milk and pandan leaf are the only 100% essentials.
If making Hainan rice then you should start by frying ginger/garlic paste, then add star anise, cinnamon, cardamom (I am not sure all of these are required), then coat the rice in that. The rice should not be cooked in water but in chicken stock from poaching the chicken. Sesame oil is not for cooking, it is a garnish, so always add it at the end of whatever you are cooking. Again you need pandan leaf in the rice cooker, and lemongrass is unlikely to be a bad idea either. You can add sesame oil when serving.