Is there a universal format for 24-hour time?

This may seem like a duplicate but I didn't find the exact answer to this, and all related answers were opposite to each other and confusing to me.

At my work (in the US) we use 24-hour format. I usually write it e.g. '1735 hours' or '17:35' (without 'hours'). I usually get corrected by supervision to '17:35 hours'. In my understanding, it should be either no colon, but 'hours', either colon, no 'hours'. Not both. Is there an exact rule I can relay to?

There is nothing I can find that specially addresses the OP's question about using 16:30 versus 1630 hours in the many organizations that use a 24-hour time for communications and records; they seem to adopt whatever conventions or portions thereof are useful to their own organizations for avoiding ambiguity, which is the purpose. Nor is there anything that says that "16:30 hours" would be incorrect.

Many organizations use a 24-hour clock, adapting it to suit their own needs for avoiding ambiguity. U.S. military time is an adaptation of 24-hour universal time. The U.S. military's rules have been worked out with allies, especially English-speaking allies (agreed to, in AmE; agreed, in BrE) for clarity and to avoid confusion. Here's a bit from an article on saying it and writing it: How to Tell Time Like a Soldier.

0001 (12:01am): “zero zero zero one”
0215 (2:15am): “zero two fifteen”
1545 (3:45pm): “fifteen forty-five”

While saying “oh” for “zero” (“Be there at ‘oh six hundred!'”) is colloquial and often seen in movies and TV, saying “zero” is a part of military communication protocol.

As far as whether you should say “hours” after giving the time, that somewhat varies by what branch of the military you’re dealing with. If Soldiers and Airmen are saying 2:00pm, they’re a little more likely to give it to you as “fourteen hundred hours,” while Marines or Coast Guardsman are a little more likely to render it just “fourteen hundred.” Across the branches though, it’s typical to drop the “hours” bit when you’re talking face-to-face and your meaning is obvious, only adding it in conversation and written communication that’s more formal and where you want to make sure the message is clear.

Also, each time zone has a letter designation. U.S. East Coast time is R. List of military time zones (Wikipedia).

The letter J ("Juliet"), originally skipped, may now be used to indicate the observer's local time.[3] This is not an international standard, and many locations/fields may not recognize such use.

The letter Z ("Zulu") indicates Greenwich Mean Time (GMT) or Coordinated Universal Time (see UTC±00:00).

They are used in conjunction with military time: for instance, 6:00 a.m. in zone UTC−5 is written "0600R" and spoken "zero six hundred Romeo".

http://www.spacearchive.info/military.htm

Writing Military Time

Different professions and types of organizations write military time differently. The military, emergency services and hospitals usually write military time as hours and minutes without a colon and often add the word "hours" afterward.

Allied Communications Publication 121

This is a publication of the Combined Communications Electronics Board titled Allied Communications Publication 121 (October 2010). The CCEB is an organization created by the United States, the United Kingdom, Canada, Australia, and New Zealand. This publication is the only official one I've been able to find; its publications are compliant with NATO standards. It discusses the DTG (date-time group) in messages:

EXAMPLE: ø9163øZ JUL 11 represents 163ø GMT on 9th July 2ø11.

This is the way messages that arrive in the Situation Room at the U.S. White House are identified. I personally have done research in presidential libraries and seen a lot of messages with this DTG.