From your point of view this is an entirely reasonable request.
Let's turn it around and look at it from your boss's point of view. He probably thinks his other employer is doing an OK job and wants to keep him, so that his business is on an even keel and he doesn't have to go to the trouble and risk of recruiting someone new. He would lose this employee if he didn't give him use of the van as the employee has no other way of getting to work and can't afford a second car. He has to have the van anyway, so that he is paying all the fixed costs for it is irrelevant. The extra gas may or may not be something he has noticed but he is apparently not worried about it. So from your boss's point of view the current situation is fine. Now you come along asking for a raise. That is money out of his pocket, for not much apparent benefit. It makes the pay between his two employees unequal, which could be a source of unease to him or future difficulty between his employees.
So far, this is one of those situations where someone doing the right thing (being responsible with their money, being independent minded, etc.) is apparently disadvantaged by that. Life's unfair like that. How can you sell your request to your employer? Traditionally, the only way (given no trade union and therefore no strike) is to find another job that pays better, or threaten to do so. Before you go that far, you can try an appeal to fairness. The more you can make meeting the request an advantage to your employer rather than just to you the more likely it is that it will be granted. Good luck.