It's not your diet, though eating healthier fats does mean your milk will have those healthy fats present. Consuming plant based fats, unsaturated fats, and Omega-3s has shown to be helpful for making lots of milk and giving baby the health fats they need to grow and develop their brain.
1. How full your breast/chest is can impact how much fat is released.
The longer the time between pumping or feed means lower initial fat content at the start of the next feed, because fat adheres to the alveoli/ducts while milk stands in the breast between feeds.
The fuller the breast, the lower the fat content of the milk; The emptier the breast, the higher the fat content of the milk. You can help this by feeding or pumping every 2-3 hours with one longer sleep stretch at night but not going more than 4 hrs between night time pumps/feeds.
Full Breast = Lower fat content & slower milk production
Empty breast = Higher fat content & faster milk production
2. Breast compressions improve fat content. Gentle breast compression helps release fat and increases the amount of milk you can give when nursing or pumping.
Breast compression: Hold your breast with a “C” shaped hand and gently squeeze your thumb and index finger towards one another. You should see baby begin to swallow when they are getting milk. Hold this 4-5 seconds then release and repeat. Move your hand around your breast to empty all the areas.
3. If you are pumping make sure you are using a correctly sized flange (the funnel shaped part that touches your chest) as the side of your nipple should gently rub on the tube to get the best oxytocin release and milk flow.
Most people need a smaller size than the standard which comes with your pump. See: https://www.babiesincommon.com/flange-fits-guide