Although this method does work you will get a better finish through the use proper tools or consider engaging the help of a professional if you have no prior polishing experience.
Brake fluid is very corrosive on paint and will damage the finish if not washed off quickly.
This is a thorough way of doing it. Note there are still fine scratches in the completed (pre-sealant) picture as this car is a daily driver and the person who polished it before took off way too much material. Trying to get a better finish was risky.