Once again this is not strictly a question about Bengal cats funnily enough. I’ve just written a post about Maine Coons making good pets and this topic is very similar.

With regard to domestic cats getting on with other cats, it is almost irrelevant that they are Bengal cats or not. What is relevant is whether the individual cat – Bengal or otherwise – is socialised (in effect, trained) to get along with other cats.
What I mean is if the cat breeder who made the arrangements to bring a beautiful Bengal cat into the world ensured that she allowed the cat to meet and play with cats other than siblings and their mother, that individual cat will be comfortable with other cats when they grow up. The same can said if the cat played and interacted with people and dogs.
It is all about making sure the individual Bengal cat gets used to being around and interacting with other animals including the human animal.
When I visited A1 Savannahs in Oklahoma (they breed Savannah cats) way back in 2008, Martin and Kathryn Stucki had these beautiful Savannah kittens running around the living room and other parts of their home to make sure they met people like me and other visitors.
This was socialising the kittens to people. These $5,000 kittens were in their first 10 weeks of life; a very formative time. Experiences at this time stick for the rest of their lives.
So, back to the question in the title: Bengal cats do get on with other cats provided the cat breeder did her job properly. And all breeders should and normally do a very good job at socialising their cats. If they did not they’d be out of business.
I used the phrase ‘almost irrelevant’ in the second paragraph. This is because it might be argued that a high filial Bengal cat is more assertive than usual as they are wild cat hybrids. They have wild Asiatic leopard cat in their blood. The connection to their wild cousin is diluted by hybridization but it is there. This may make it more important that breeders fully socialise Bengal cats as the Asiatic leopard cat is very independent.
The CFA breed standard for this breed states that the cat is alert and active with inquisitive dependable dispositions. This activity level and what I would call ‘wild cat intelligence’ (in F3-F1) may make the Bengal less naturally good at getting along with other cats than other cat breeds because they might be less laid back. And high filial wild cat hybrids are a bit larger than average and strong. This may go against calm relations. I could be wrong but this is a gut feel.
You don’t need to buy a Bengal cat or any other purebred cat to make sure they get on with other cats. Random bred cats are almost always socialised one way or another and make great pets too.