Yes, dying is demaging to your hair. If you're hair is already heat damaged (because of the straightner) the dye gives you extra damage. Only you can decide if that's worth it and what the condition of your hair is. Some curlies can have more dye/heat/sulfates and all other things that damage hair then others. If you have fine and/or porous hair, your hair will be probably very prone to damage.

Do you follow the CG method already? That can make a huge diffrence for the health of your hair.
highlighted 3a hair. Fine strands, medium to high density. Probably high porosity. Growing uit bad layering and aiming for waist lenght!

Pre-poo: coconut oil
wash: CJ Daily fix or SheaMoisture Coconut&Hibiscus
RO + LI: different every time
Styler: CJ Pattern Pusha, CJ CIAB

dislikes: glycerin in low dews, scissor happy stylists, magnesium sulfate

(modified) CG since june 25, 2012
Hiarfinity + extra MSM since March 5., 2014

SL - APL - BSBL- BSL - MBL - WL (stretched)