I was able to claim compensation but only with a Lawyer, and then only when the Lawyer reminded AB after the first letter announcing the submit of the formal law suit with the competent tribunal.
I personally don't see the need to use such agencies like Flightright. These are usually crystal clear cases that you can only win, and if it's not crystal clear the agencies will not accept your claim anyway. At least in Germany, if you win, and you will, then the airline needs to pay for your lawyer costs anyway. Just go with a specialized Lawyer. Some airlines will just pay if they already see which lawyer is sending them a letter
The LBA can not do anything for you. They could in theory fine the airline (but will not do it anyway) but they can't force the airline to pay a compensation for you. This is not what they are there for.