The principle behind a brainstorm is that one idea leads to another, and another, and another. A mindmap is simply a page where you write down all your ideas as they pop into your brain, arranging the words around the page. A way of grouping similar ideas together and putting down further thoughts an idea generates. It's an ideal approach to the daily painting ideas.
Start writing anywhere on a page, putting down the key idea or concept, then put a circle around it. (In my mindmap shown in the photo, this was the word "Journeys".) Now write down the first thing that comes to mind when you think about the concept. Don't censor yourself, don't reject some ideas as "bad" and try for further "good ideas". You'll weed out the more useful ideas later. At this stage, your task is simply to write the first thing that comes to mind, then the next, and the next.
If ideas are related, group them together. If they're different, write each down in a separate section of the piece of paper. There is no right or wrong way to arrange your mindmap; do what works for you. Put each idea in a circle, or a square, star, picture frame, whatever. Group ideas together. Sketch pictures. Use different color pencils.
An advantage of brainstorming by using a mindmap rather than a list is that its structure is more informal. You won't feel restrained by a neat list, hesitant to add an extra thing that then makes the list look untidy. Think of the difference between a map and a route description. When you're looking at a map, your eye can take in any section at any time, showing you various options. With a route description, you have to follow one step at a time, to do exactly as you're told. A mindmap is a map of ideas for paintings, all sorts of different routes you might take from the initial concept.
How long should you spend brainstorming? It's tricky to say, but at least 10 or 15 minutes. Think literally, think laterally, and force yourself to keep going. Because one idea will lead to another, often somewhere surprising. Don't obsess about being neat, don't worry about your spelling or handwriting. You're creating this for yourself, not an audience.