Male amazons tend to be ruled by hormones which can lead to some serious territorial or possessive issues. I think you have two major options. #1 is to consider him a pair bonded bird which means he may be better off being allowed to enjoy the company of his mate and be more of a look at pet. There is a high probability that as long as his mate is around, he will be aggressive toward humans. #2 is to separate him from his mate such that they can no longer see each other. This option has a higher probability of getting him to be a handleable pet. However, some older males that have been pair bonded for a long time may never come around be being really personable. In my mind, if his mate is another amazon, then I'd be inclined to discourage breeding while accepting him as a look at pet and let him just be a happy bird with his mate. If his mate is the quaker or conure in your picture, then I'd take a hard look at behavior and safety of the smaller bird. When in doubt, I'd at least put them in separate cages and limit physical contact time. In which case, it might just be best to move him to another room and try for option #2.
One helpful hint when it comes to winning over the trust and kindness of an amazon is to not try too hard. If you push yourself at the bird, they are likely to push back. In other words, don't harass him trying to make him like you. Give him the option of coming toward you or accepting treats from you. Don't push too much. As you may be seeing though, you have to balance this with not letting him push you around too much while also trying not to get bit. Some people have a better knack for this than others. If they learn they can push you around, then the aggression may just increase. But, if you try to be a tough guy and get bit, he'll be more likely to keep biting you. This is a hard balance to strike and tends to come down to the type of body language and personal style some people have. Like, I said, if he's happy with a mate, letting him just be a look at pet and be happy being a bird is an entirely valid option.
If he steps up for you willingly, give him some low key praise, talk to him without pushing for more and put him down with a treat before he has a chance to get wound up and bite. Only after he's reliably willing to step up and be on your hand for 30 seconds or a couple minutes without biting should you think about pushing for more. Don't over stay your welcome. Amazons are independent and don't actually want a lot of holding unless they have already decided they like you a lot. Even then, many amazons would rather keep it brief even if they think you are their mate. Watch body language. If he is flashing his pupils or flaring his tail, don't even try to pick him up. Just keep it to verbal interaction. If the house is calm, he's calm, no one and nothing he dislikes is around, that is the time to ask him to step up. I say ask, because you should be willing to take NO for an answer. Remember the part about not pushing, and don't over stay your welcome. When in doubt, keep it positive and back off before he decides to make you back off.