Just to help you avoid painting yourself into a corner, as it were, it's important to remember that Bangladesh ≠ Bengal. Bangladesh is only a part of Bengal so its flag isn't the only OTL thing you can draw on for Bengali flags. Even more so, the earliest version of the OTL Bangladeshi flag only dates from 1970.I will do that next, PolishMagnet. I actually tried to design a Bengal flag before the Burma one, but after a long struggle I can agree with you that redesigning a Co-Prosperity Bengal flag is hard. It's unfortunate that the Bengalese color scheme is so...dull, shall we say.
The Indian state of West Bengal doesn't really offer much, it's only got a seal (no flag). But the Nawabs of Bengal had their own flag, as did the fully independent pre-Mughal Bengal Sultanate. Colourwise they're both just red and white, but they'd give historical grounds for adding white to the mix and escaping the eye-jarring red-on-green.