First, have a careful read of the building or association by-laws. The process to change the by-laws should be defined; it is this framework you need to understand.
For instance, I live in a house not a flat, but the house is part of to a group of houses that form a Quartier and so there are rules and regs that limit my use of my property. Common assets, exteriors, use of our properties are regulated by a Quartier 'consititution' - or whatever it is - written when the houses were built. This defines what regulations need a unanimous approval to change, and what only requires a simple majority. One property = one vote, so he who owns the most property wins. Renters do not get to vote, only property owners. But that's my Quartierplan - YMMV. You need to understand the legal framework around changing the building rules.
(If the other dog owners are renters whose voice does not count, contact the owners of those flats - they have a vested interest in the status quo, as banning dogs would likely mean that their tennants would move out, representing a financial loss to the owners.)
I've had to deal with the antics of a dog-hating neighbor. For what it's worth, here is what I have done:
First: Be a shining example of responsible dog ownership. Be respectful of others at all time, always keep your dog leashed in common areas, clean up after your dog and all others, observe offical quiet hours scrupuously, keep your dog as quiet as possible even during the times everyday noise is allowed, enroll in regular training classes so as to have proof proof that you are acting responsibly - in short: never, ever give anyone in the building cause for complaint. This is your best weapon in the war of hearts and minds.
Second: In most other disputes I would counsel compromise and 'good neighborliness' to preserve harmony - but this is an exception. Gloves off. Seek legal counsel, and be prepared to fund the expense. Many folks will back off at the prospect of a potentially expensive legal wrangle.
If either of the above are not possible, put your flat on the market and move.
Because even if you win the official battle you still have to live with dog haters who have the unofficial means to make your life - and your dog's - a misery.
I hope a solution can be found, and wish you all the best.