Shut the fuck up and wait for instruction.
When you're in the conspiracy stage, you need a cell like structure to protect the conspiracy against double agents and detection.
When you go live, you decapitate the local flavor of secret police, arrest the leader, and start rounding up or killing the key players.
Then talk.
But I fully agree with your subtext: it's not a technical problem.
There's the problem, nowadays when you go live you'd have to be able to move faster than the electrons that communicate that something is happening.
Which means you need to first remove or impair your target's means of communication, which means you need to go live before taking action.
It's turtles all the way down.
It really depends on who you are trying to depose. I wouldn't trust any device if you were going against the interests of America / NATO, there are just too many opportunities for side channels. Likewise if it were using Chinese hardware against China. Assume you're compromised in either situation regardless of how secure your encryption seems to be.
Article from 2015 talking about phones shipping from Chinese manufacturers with backdoors already installed:
26 Android Phone Models Shipped with Pre-Installed Spyware
http://thehackernews.com/2015/09/android-smartphone-malware....
Signal also had some sort of work towards preventing contact list disclosure.
At a state level, there's also traffic analysis. If you find Target A then look at their traffic, you might be able to time-coordinate messages sent to other users. (Target->Signal Servers->Recipient)
Guess they could take the Signal source and run their own copy of it, too, eh? I'd also add a time-based auto-wipe function to Signal, which is useful if your are suddenly captured. Doing it by hand is tedious, so people don't. Signal doesn't do this because they don't want people to think it implements a secure remote wipe. But they should consider the problem of an activist having their phone recovered. If the app would delete on time, it'd mitigate some damage.
Telegram shouldn't be touched.
But remember that Turkey is a NATO ally, so you're up against the NSA, CIA and MI6 for starters (in addition to the fine intelligence service of Turkey).
So I would think that Signal would have to hand out all registered phone numbers in Turkey - a list which could be checked against all military personnel. Given that they've detained thousands of teachers, I don't think they'd be above detaining thousands of suspected troops, even at the risk of waterboarding loyalists.
You don't need an accurate list, just some help "short listing" people.
Similar issue with Tor - if you're in the military and your mobile device used Tor before/during the coup, you'd be on a watch-list (or shot).
The best op-sec is the terrorist/stay-behind/contras: small independent cells, with no knowledge or communication with each other. Obviously some plan is needed to set up a command and control structure when the coup is "won". I don't think there are any great solutions here, that also doesn't leak enough meta-data to get you tortured and killed in the event of a failed coup.
A modern, digital scheme similar to this is called 'chaffing and winnowing' [2]. Both are steganography rather than encryption, but the intent is the same -- to communicate securely over an insecure channel.
[1] https://en.wikipedia.org/wiki/Null_cipher [2] https://en.wikipedia.org/wiki/Chaffing_and_winnowing
OTR messaging is encrypted (only intended recipients can read your messages), authenticated (you can verify intended recipients identity), deniable (anyone can forge messages after a conversation to look like you sent them), and forward-secret (if you loose your keys, previous conversations aren't compromised).
Also, it is wise to communicate as little as possible. Chatter can be detected to see who are involved. It often doesn't matter what you said, if you were involved or engaged with the wrong people, you may find yourself zip-tied in a stress position.
As one of the other commenters said, WhatsApp and Signal still rely on third parties to host the system. But doesn't Signal simply have each device generate a private key that it claims it never knows about so even if the Signal server were hacked it still wouldn't compromise existing keys?
PGP (or Keybase.io) seems like too much work for non-techies.
I'm not as familiar with Telegram.
In the end, could you do any better than a trusted third party providing a protocol it claims generates keys on your device and doesn't share them?