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So, here are a series of exercises that will help to develop your ability to rap and write lyrics. One very simple exercise is to open the dictionary to any page, and then pick a word, and then try to come up with two to three words that can rhyme with that word. Alright? That's one. Strengthening your ability to find the rhyming word to any word that you want to find.
Another thing that many rappers do is something called freestyling. Freestyling is pretty much like improvisation, or rapping where you play a beat, or just do it a capella with no music, and just try to create a rap without thinking.
One of the biggest obstacles in strengthening your rap is thinking too much, because the thinking mind actually shuts down, sometimes, creativity. Creativity is more from your heart. Just off the cuff, just organic. And by freestyling, and coming off of the head, as they say in hip-hop, you start to develop your ability to just put together ideas and words.
Another way of developing your rap style is studying literary devices and how you can quickly put together some things, like metaphors, similes, hyperboles and personification. These things you may find in English class, but they actually can be used in developing your rap style.
The last thing that you could do, in terms of developing your ability to rap, is battle somebody else. Like all sports, competition helps to make us better. And, unless sometimes you have somebody to go against, it doesn't allow you to step up to a level that you didn't even know that you can do. Like the term goes, "steel sharpens and steel", sometimes you need the competition to be better.
Those are some ways that you can strengthen your ability to write songs and become a better rapper.