Screamo style singing is a learnt skill and should not be attempted before training your voice in other vocal styles. Once that is done with the help of a vocal coach, you can learn to sing screamo by applying the same techniques you would for any music genre, including jazz, blues and gospel, without causing temporary of permanent damage to your vocal cords.
Find and stay in your vocal range of either alto, soprano, tenor or bass when learning to scream sing and use your false vocal cords to produce sounds. The false cords are folds of mucus membrane just above the true cords and help protect your true cords from damage when singing screamo style.
Warm up your voice the way you would for any type of song for 30 to 40 minutes, using the vocal scales you have learnt from a coach. Concentrate on breathing for at least 10 minutes, taking air into your diaphragm and not your chest. Think of this as warming up any muscle you would before a work out. This will both relax and stretch your cords.
Increase volume gradually, rather than jumping straight into screaming, at first forming catlike growls as you get the hang of it. Eventually you will learn to produce nasal sounds from the front of your throat and sinus region, which will go easier on your cords and help you sing safely. As you move from these primitive sounds, you will start to articulate them into actual words.
Keep a warm glass of water on hand and drink in intervals to keep your throat moist and your chords open. Cold water will not work as well as warm and can do harm.
Avoid milk and dairy products as they will coat your throat and let less air in. Any time you feel pain or irritation while scream singing, stop immediately and rest your voice until the discomfort has subsided completely.