Absolutely nothing, really, that you can do.
If people have primary childcare responsibilities and have been given flex rights, the company cannot then reverse them so those without those rights have to then share what's left. The only way to avoid that is to request flexi rights yourself (if you are a primary carer).
Someone else is then getting their pick of what's left, because that person is valued more than the others. The only way to change that is to also become highly valued, and that's down to you. You need to put in the legwork and show the loyalty to move up the favoured ladder. You would only have grounds for complaint if you feel you can prove that you are being discriminated against because of gender, age, sex etc (relative to others like you who are not on flexi working).
These days it is no longer about equality (treating everyone the same), it is about diversity (enabling, and accounting for, differences such that people are able to perform to the best of their own abilities). There will always be winners and losers in the situation you describe, and the HR trick is to ensure that different payscales for 'unsociable' hours are set at levels that generally manage to match the supply/demand of staff. It is very difficult to keep that in balance all the time.
If you wanted to challenge it, you may have grounds for complaining that you are being discriminated against on grounds of age (assuming favoured worker has been there years), but this would be a hard one to prove, as they would counter (for example) that she is there because she performs well or has established a precedent for doing those hours or has the lowest sick record or a dozen other reasons...