Yes, he's Chaotic Evil.
To understand how you get there, you have to dispense with your feelings. This isn't about how you feel about him, but whether or not what he says conforms to absolute definitions. So, let's define those absolute definitions.
1) Good: Desires above all else the ability to create, heal, and build up. It seeks above all other things well-being and health. Believes evil to be a non-thing, merely the absence of good.
2) Evil: Desires above all else the ability to destroy, and to bend other things to its will by force. It seeks power before well-being and health. Believes good to be a non-thing, an illusion and a lie.
3) Chaos: Considers the good of the individual greater than the good of the group. Indeed, probably considers the group to be a non-thing, merely a way some people manipulate others to get what they want. Considers the internal self - the conscious - to be the source and seat of moral judgement and meaning.
4) Law: Considers the good of the group greater than the good of the individual. Indeed, probably considers the individual to be a non-thing, an illusion of separation brought about my ignorance or brokenness. Considers the source of all meaning and moral judgement to be external and residing in some higher power.
So, there are definitions. Where does our character fall in this spectrum? To answer this question we have to ask what is the essential nature of the character, and to answer that question we have to answer the question, "What will the character choose when push comes to shove and he finds himself in a hard place?" Using that question, we can strip away the characters pretences, personality, weak beliefs, convienent beliefs, affectations and so forth, and look only at the core alignment within. Where in the speech are the alignment cues, where the player reveals his most inner convictions?
It's easy to get distracted by this and think that declarations of loyalty to some group are strong and perfect predictions of lawfulness: "I'm a knight and my Brotherhood always goes first..." Not only can a chaotic feel loyalty to his friends, close friendships and intimacy are almost always the mark of chaotic society rather than lawful society. Lawfuls are bound by shared duties, and not by their feelings for people. There duty is more important than their feelings. When examine the knights claim that "my Brotherhood always goes first" in context, it's hard to see this knight as either honest with himself or the audience or bound to the order by a sense of duty or some larger purpose. In fact, he immediately says it himself: "I
love all my brothers..." A lawful would consider his personal feelings about the order to be irrelevant, and his personal feelings not particularly worth sharing in comparison to declarations of his devotion to the cause or the requirements of his duty and honor.
And he immediately goes on in this vein, because the next thing he does is complain against the existing social order:
"Some of my brothers go from battle to battle and war to war but they always let
those greasy nobles - whom are NOT our brothers! - to come and rule the lands which WE have liberated!"
Again, he is not focused on the lawful right of the nobles to rule, but on his feelings and personal frustrations. A lawful mind would consider those feelings shameful, and certainly would not be willing to share what he would consider dishonorable temptation to overturn the established order.
He continues....
"We should rule the peasants because it's easier to protect them if we have the power."
Now this is the first truly lawful statement he has made. He declares that motivated to a purpose - protecting larger society of which he is a part. But that declaration of purpose is immediately undermined by two more important things, and the first is his admission that he's not actually motivated to protect the peasants.
To tell you the truth the peasants are completely meaningless to me but I still pretend I care...
Once again, this character wants to share his feelings about things, and his honest when it comes down to it feelings are.... he doesn't care about the peasants. Do you think that when it comes time to choose between himself and the peasants, that he's going to choose society over the self? Does seem like a self-sacrificing sort of character? What about the larger society versus his close friends? Again, he seems to prize his private and personal relationships over his public duties.
My dream is to seize all the power to my brotherhood and rule with an iron fist
To me this is absolutely the strongest statement of alignment in the whole story. When we boil away the characters pretenses and affectations, ultimately he is motivated to claim personal power and rule over everything else. This is the ULTIMATE declaration chaotic evil intention. His dream is not to serve others, but to serve himself and force others to do his bidding. His dream is not to serve something larger than himself - a diety, a nation, an idea - but to obtain individual authority.
will say that I want to do this little by little without bloodshed, but if someone suggested that we kill all those in our path, I would not object.
Again, this is a strong statement of alignment. While the character would like to avoid bloodshed, when push to comes to shove, he's willing to kill everyone to get what he wants. He's stating what he really cares about and what he'll really choose when he's forced to choose.
There aren't many of those of my brothers that are truly loyal to the brotherhood.
Here I think we have a twisted and self-serving definition of 'loyalty'. He's actually forming an inner secret cabal that is primarily loyal to each other, and not to their lawful leaders. This loyalty isn't based on adherence to an external reviewable code - after all it's effectively a secret society with its own rules that it has made up for itself at this point - but based on interpersonal relationships. 'Loyalty' here is an affectation which is far removed from its plain meaning - obeying his superiors and doing his duty. He wants to have a coup. That's not loyalty; that's rebellion.
I tell them of my true intentions: My dreams of power and glory, the new dawn for our brotherhood.
'The dawn for our brotherhood' is again pretence. Notice just how more prominent personal pronouns are in that declaration: I, my intentions, my dreams.
What we have here is a CE individual who has inflitrated a lawful organization of some sort. Exactly what the alignment of the organization is hard to tell. The individual seems to me to be very intelligent, but probably has a fairly low wisdom. He doesn't really know his own mind and he's not particularly self-reflective. He may not even know his real alignment, and he may sincerely believe he is 'lawful' or even 'good' as he understands the term. But ultimately he is a decietful traitor, motivated by dreams of personal power and glory. Like most chaotics that aren't completely pure in their nature, he still has affection for those which he has a friendship or kinships, but its hard to believe that he won't, with a show of regret, kill any 'friend' that gets in his way when push comes to shove. Other members of his order may believe he is lawful, as he outwardly presents himself, and some may believe he's actually fanatical in his beliefs. A few probably suspect what really lurks in his heart, but might be afraid to speak out.
It's a complex and interesting character, but its by no means at all 'lawful evil'. Evil yes, but not lawful in the slightest degree.