Me and my friends have been playing a Hellknight themed campaign in PF2e for about half a year now. We're on session 24 right now and there's definitely many obstacles we've had to deal with in regards to trying to figure out answers from the material available across many books. Naturally we went to Path of the Hellknight from first edition for the basic information, in which every play read it cover to cover and we selected Order of the Nail for our campaign. Our group spans alignments, Lawful Neutral, Lawful Evil x2, and Lawful Good. This hasn't been much of an issue because since we're all Hellknights even if we don't exactly get along we all work for the same order and that is extremely effective in terms of keeping us on the same page. If anything this group has been more cohesive and unified than almost any other campaign I've played in because everyone was on board with the theme and we're operating as Hellknights.
So what could be the problem? Well, the answer is that the source material for what is supposed to be a rigid organization that follows absolute law is surprisingly vague on many, many facets that actually affect play at the table to a significant degree. It doesn't actually describe any of the laws or restrictions that are put upon Hellknights or any examples of how Hellknights deal with other laws that contradict their own. It says Hellknights hold Hellknight law above all other law, and they hold others to the expectations of the Measure and Chain as ruthless enforcers of the law, but it doesn't give an example of how they actually deal with other governments or nations (beyond ignoring them if they think they're wrong.)
There's no examples of how Hellknights actually punish crimes. We had to scrounge the internet for something that seemed to function as a general guideline for common crimes like theft, murder, assault, destruction of property, etc.
There's no examples of when it's okay to use people for devil sacrifices. It says they don't serve devils, but they definitely do summon them as tools. The Hellknights have authority to forcefully conscript people into military service or labor for the cause of fighting chaos, and if they can forcibly put someone on the frontlines to die, it doesn't seem like much of a stretch to say they can forcibly conscript someone to being a sacrifice for a devil who is going to be more useful in an upcoming fight than the person that they conscript. However, it doesn't actually say what their stance is on this in general and for any order other than Order of the Gate, who it seems considers this standard doctrine.
It doesn't say what to do with wealth that's gained from fighting off monsters or enemies. If trolls raze a town to the ground and take all the wealth, and then the Order of the Nail tracks them down and kills them, is that wealth considered the same thing as stolen goods, or is it considered something different? Obviously the Hellknights aren't a charity and they could easily just consider it a charge for their service of killing the trolls. Yet, that's just an assumption, it's not actually backed by any sort of useful information within the source material.
In summary I feel like with the product there was a design decision to not tell GM's and players how to play their characters or run their campaigns. So instead of actual hard rules and guidelines there's instead a lot of vague concepts that are up to interpretation. I think in this specific product, and in Hellknight products going forward this is a definite mistake having actually played a campaign using it. The Hellknights are a rigid order of doctrine and law, and it's very difficult to play a game when you have no laws or doctrine to refer to. There's no explanation of the ranks and their actual duties or responsibilities. There's no small "handbook" of how you should conduct yourself, when you should have your helmet on, when you should wake up, expectations of drinking or overeating or whatever.
In my opinion the book should be basically designed for rules lawyers to use and abuse, because the Hellknights ARE rules lawyers and that actually supports the gameplay of playing in a Hellknight order.