It is definitely true that when you bring home a new bird, especially if the bird is not a hand-raised/tame bird, that if you clip them it will make taming, bonding, and specifically "earning their trust" much easier and quicker, simply because #1) The bird cannot continually fly away from you (and just as important, you won't be doing the usual action of chasing them all around the room from window to window with a towel, which really serves to make their distrust of you even more intense)...Also, when they cannot fly they tend to lose that typical feeling they have of being the "dominant" one in the room, especially if they are on the floor and the lowest thing in the room; that's when they tend to give-in and trust you most-often, when they need your help to get back up to their cage/territory and to not be the "lowest thing in the room", as they hate that...So yes, in my own experience it does help tremendously with earning the trust of a non hand-raised and non-tame bird, forming a relationship with them and bonding closely with them.
***All of that being said, clipping the wings of a bird who is already hand-tamed or that you have already bonded closely with in order to help to "train" them to do certain things, or to curb any aggressiveness that they may be displaying does not always work; it may help, it may not. It might make things wonderful and solve all of your problems, or it might not do a thing. I've not ever seen it make the situation worse, but I've not clipped the wings of many already-tame birds for that purpose, my experience is with hand-taming very young birds who were parent-raised and not socialized with people at all, and I have had great success with using a very conservative wing-clipping of only the outermost 5-6 primary flight-feathers and then working with these birds on a regular, daily basis for the 1-2 months that this type of conservative clip will give you...However, as far as your situation goes, doing this type of conservative wing-clipping on your already-tame BFA in order to work on curbing his aggressiveness may work wonderfully well, quickly, and make your relationship with him much, much stronger...or it may not help one bit. There's no way to ever know in your type of situation unless you try it out...Like I said, if a conservative clipping of only the outermost 5-6 Primary Flight-Feathers on each wing is done, they will grow back-in fully within 2 months or so max, so if you were to do it, you have to take full-advantage of every single day you have to work with him in that very short time-period of only 2 months, and that's usually the maximum, it depends on how quickly your bird's feathers grow-back in, and also how close to having a natural molt he is when you clip him...
****I'm not telling you that you should clip your bird's wings to try to ease his aggressiveness, and I'm not telling you that you shouldn't do it. I'm trying to simply give you BOTH SIDES of the wing-clipping story, which often don't get told, often whenever this topic comes-up, as soon as "wing clipping" is typed, people get upset and emotional, which is understandable for sure...but the facts are the facts, and we should be fair and present both sides of the story...Clipping your bird's wings in not at all painful for them, it will not cause any permanent damage to their feathers, it is completely temporary, and most important to keep in-mind and make sure of is that when you do clip your bird's wings that you have someone who knows what they are doing do it, and that you request, no, that you DEMAND that they clip BOTH WINGS, and that the ONLY clip the Primary Flight-Feathers, they don't go into the Secondaries, and that they only clip at-most the outermost, I'll say 4-6 Primary Flight-Feathers, as this will ensure that your bird can still glide across and down with total control, and so they will glide softly and with control to the floor instead of dropping like a stone, and that they just will not be able to gain any altitude...And it will also ensure that your bird's feathers will grow back in fully in at-most around 2 or so months...That's why it's important that you take full-advantage of every day you have with your bird's wings clipped as far as training them, working with them, spending as much time as possible with them, etc., because you don't want to have to clip them again.
****Something that I feel strongly about is that we all be respectful of BOTH SIDES of this discussion whenever it comes up, because everyone is in their own situation and must make whatever decision is correct for them, their bird, and their household when it comes to clipping their bird's wings. There are many circumstances where it's actually much safer for the bird to have their wings clipped full-time in certain households; The best example of this was written here not long ago by a very beloved member of this community, when they told their story and explained why they keep their very loved fid's wings clipped full-time, because their spouse, who is home all day with the bird, has some physical disabilities and cannot go chasing the bird around their home every day, and if their bird wasn't clipped it wouldn't be a safe living-situation for him in their home...and trust me, this bird is loved in that home as much as any human-child could be...So I just think it's extremely important to always take a step back and put ourselves in the shoes of others and think about that BEFORE we say anything out of strong emotion and passion on the topic.