You either need to use fewer products/ ingredients that build up or shampoo more effectively, it's your choice which. Yes sulphates are drying but TBH flat ironing is way more damaging. Have you considered wet wrapping for heat free straightening? It's possible your hair is "dry, frizzy, horrible ... tangly
" partly because it's damaged from all the flat ironing. Are you at least using a low setting on your iron?
You can still use heat protection without piling silicone on top of silicone, you should only need one product that contains it. Silicones are not the only ingredient that can act as a heat protectant, other ingredients can including hydrolysed protein, propylene glycol, some polyquats and glycerin. There are also other ingredients that can provide 'slip' whilst penetrating and patch repairing damage from either heat or bleach, including hydrolysed protein, ceramides and panthenol. You might try getting a better balance in your routine.
You do not need to conditioner only wash to be Curly Girl, the book permits shampooing with sulphate free shampoos and I *think* the latest edition permits the sort of silicone that does not build up. Cocoamidopropyl betaine can handle silicones providing you use some massage. At least pick up a few more of the techniques like finger detangling in the shower only whilst slathered in conditioner, combing contributes to mid shaft splits.