Which brand is more solid, a brand with guidelines that are fixed, or a brand with more flexible guidelines that can be subject to change? And why?

I would interpret guidlines as a brand strategy, and the answer will be yes for a brand with a strategy, clear promise and well defined target segment. Flexibility comes within a strategy when a change is needed to cope up with market changes.But a brand without strategy,  will lead to something like a try and fail approach and this brand will not be able to stand out among the crowd.

Solid Word itself answers your question completely . Brand is Solid with proper guidelines because it is working on principles and have studied till grass root level . Keeping all Pros and cons into account have framed these guidelines .

With the passage of time all guidelines should have flexible content because hope you would believe - Things which were Luxury yesterday is need today & that will go on till this life is moving .