Yes, pets are allowed on the (flex)bus for free. You must Keep your dog on a leash and place it on your lap or on the floor. If he needs to put on a muzzle. Other small animals (e.g. a hamster) are allowed when they are in a cage. Cats in a cat harness are also allowed.
You must supervise the animal that you take with you in a De Lijn vehicle. You can be held liable for the damage or pollution caused by your animal, unless it is proven that the damage or soiling was caused by an error van De Lijn or another party was caused.