So, as the title asks, would it destroy the idea of the beautiful bi pride flag to write "PRIDE" in the colours and have the background filled with for example other colours?
So you're saying something like the rainbow band flag, with PRIDE in blue, purple and pink letters or gradient? I don't think it destroys the concept by any means, but I think it would be visually busy. I like the bisexual pride flag for its colors and also its simplicity: three bands, three colors.
It wouldn't destroy it. If you're worrying about breaking some etiquette rule like with a national flag, I don't think it applies. The simple color scheme is useful enough to be applied to other graphics.
