The Amber military is under the command of the king, with individual commands usually delegated to a prince or Duke whose men make up the bulk of the command. Historically, overall command reverts to Benedict when he is available, but given his comings and goings make that an unreliable command structure.
Amber maintains a certain amount of a standing army for civil defense, but it is skeletal, with the assumption that it will be reinforced from the noble houses or from shadow as needed. The standing commands exist for specific purposes, and it is a token of respect from the throne to be granted one of these commands.
The Rangers of Arden
The rangers are probably the most famous of Amber's commands. Protectors of Kolvir, they are responsible for protecting the roads and paths of Arden. Beyond those mundane concerns, they are Amber's first line of defense against threats out of shadow. It's not just a matter of watching out for enemy armies - sometimes darker things find their way in. This has put them directly in the path of the latest threat, and most of the skirmishes to date have been between the Rangers and the invaders in the dark places of Arden.
Commander: Prince Julian
The Knights of the Oisen
The Oisen is the major waterway of Amber, with tributaries throughout the fertile eastern half of Amber. The Knights control a number of forts along the river and are responsible for patrolling the rivers to keep them safe from bandits, make sure bridges and fords remain in working order and keeping an eye out for any troubles that may emerge. They're headquartered in Garnath, and seem to be in the path of the current incursion.
Commander: "Knight Commander" Kincaid
The Defenders of Kolvir
This is a small unit with a reputation as one of the more elite in Amber. They're responsible for patrolling Kolvir and the mountains to the north. It would be little more than a minor command, but it has a historical association with prince Benedict that grants it a certain air of excellence, which they strive to live up to.
See their wiki-page for more.
Commander: Beatrice Solaris, acting CO
The Amber City Watch
The Black Gulls of Amber are not exactly one of the most well-respected commands available. Tasked with keeping the peace in the streets of Amber, they are considered decently efficient and tolerably corrupt. The watchmen are generally recruited from the enlisted ranks of the army and navy, offering employment for those whose temperament and skillset would otherwise drive them to a career as legbreakers and enforcers. That is not to say that it is a force composed entirely of thugs - the officers are well seeded with third sons of nobility and the blood of merchant houses, all of whom are keenly aware of the importance of the Wheels of Amber city turning smoothly.
Watch Officer: Tessa
The Palace Guard
The Hounds are the best of the best, or so they will tell anyone who asks. Recruitment into this command requires distinguished service elsewhere in Amber or a personal recommendations from someone with the King's ear. Entrusted with the safety of the palace, the throne and the secrets of Amber, it is necessary that the hounds be capable and loyal, and an officer's commission in the Guard must come from the King's hand.
The Order of Clarity
Founded as an idealistic order dedicated to justice, it has evolved along more pragmatic lines over the centuries. The Order has an untarnished reputation for honesty, which has resulted in them being the default choice for arbitration. As dramatic as that responsibility can be, their more mundane duties are perhaps more important. Their reputation for honesty resulted in them serving as a certifying agent for merchants, and eventually falling into the service of the exchequer in an auditing capacity, especially in places and times when the task was aon the generous side. Between these responsibilities - arbitration and auditing - the knights are a powerful organization, but are greatly limited by their own strictures. Should they ever grow too political, it would undercut their carefully maintained position of neutrality. In times of great danger to the realm, they are also called upon to act in a military fashion, though these callings are quite rare.
Commander: Acting Knight Commander Fiamme
Founded as a unit of irregulars who served under Prince Finndo, the Extraordinarii's primary purpose was twofold. Outside of the traditional chain of command, it allowed for a certain amount of military flexibility, and by serving as a proving ground for foreign nationals of every stripe, it was a way for foreigners to earn titles, status and respect in Amber, even in times when the army was not available to them as an avenue of advancement.
The Extraordinarii's heyday ended with the death of Finndo. Oberon occasionally lifted the banner again, assigning it to a specific commander in hard circumstances, but these situations, the banner mostly served as a simple legitimization of mercenary forces. Over time, the title Extraordinarii Primus joined the collection of other titles that get handed out to those who have pleased Oberon.
Commander: What an interesting question
(The admiralty does not have its own flag - the ships of amber bear Amber's flag)
The admiralty has a wide array of responsibilities. In wartime, the Admirality oversees the navy, and during peace, it has a great deal of influence on day to day maritime activities, making decisions about patrols, docking and so on. Historically, this duty carries enough responsibility that the Admiralty has been split into the Northern and Southern fleets. Cynics note that it also carries enough power that the split served two purposes.
After Corwin's attack on Amber, the combined Admirality was placed under Gerard's command, though the split between the Northern and Southern Fleet is still deeply embedded in the culture of the navy. At various times since then, command of the fleets has passed between Caine and Gerard, and at present, Gerard commands the Northern Fleet and Caine commands the Southern Fleet.
- The Northern Fleet - In addition to the seas near Amber, the northern fleet oversees the shadowpaths to Kitezh, Sukho, Begma, Jade and Tanus.
- The Southern Fleet - In addition to the seas near Amber, the southern fleet oversees the shadowpaths to Minos, Lyonesse, Cibola, Alhambra and Pathi.
In addition to patrolling the shadowpaths themselves, the Navy also enforces customs inspections. All of the shadowpath entrances on the Amber side are patrolled by picket lines of Navy ships. Ships entering Amber are boarded and inspected, and the captains given the necessary paperwork for customs duties. The captains settle these accounts dockside, or give the paperwork to the factors of the Houses or merchant companies that they work for, letting their superiors settle their taxes en masse. The at-sea inspection is intended to ensure that ships do not use Amber as a waypoint between two shadowpaths without having a tax assessed. It is possible that the Navy will miss inspecting an inbound ship, of course. Paperwork must be presented to dock in Amber, though, and a harbor-side inspection will be done if a captain is missing the necessary paperwork.