There is no way to turn curly hair straight without heat or chemical, but there are ways to naturally loosen the curl. Try these natural relaxer to naturally straighten hair. While they are not going to have the same straightening results as a chemical relaxer, it's certainly a safer more natural approach.
Amino Acid Treatment2 part yogurt
1/2 part baking soda
1/2 part Braggs Amino Acids
Baking Soda Loosener1/2 cup of baking soda
1 cup conditioner
leave on for about an hour then rinse out.
Yogurt/Honey/Bananas Mix1/2 cup yogurt(or sour cream)
2 tablespoons honey
1 mashed banana
Coconut and Lime Treatment1 tin of coconut milk
2 tablespoons of extra virgin olive oil
4 tablespoons of lime juice
2-3 tablespoons of cornstarch