Edit: The below is no unnecessary as Telegram for iOS now supports VoiceOver, and it mostly works!
My wife is blind and tried to use Telegram. Only then did we realise how inaccessible it was; which is bizarre for a text-focussed messaging app that seems to use standard UI components.
I did some digging and saw that the interface is custom and there is close to 0 provision for VoiceOver.
I have raised tickets/issues on the main Telegram code repositories pointing out the problem and sent emails to the telegram team (a handful of programmers based out in Dubai). I see there's not been any response so far but one more voice may help.
I've also evaluated the few 3rd party telegram apps on iOS - most are very old, or are nothing more than simple clones of Telegram itself with the same accessibility issues. One app 'Bettergram' looked promising at first as it's only just been released and the developers have created their own UI, but sadly, it also has no support for VoiceOver. However; it may be easier for them to add accessibility than the developers of the official app. I've contacted them asking if it's being considered.
I know IM+ has been suggested as a way of accessing Telegram - but this looks more like simply a 'shell' around the web version of Telegram.
I have found a possible alternative:
There's an app called Riot.im; it works with VoiceOver and is being actively developed.
Riot.im allows you to access a service called 'Matrix' (matrix.org). Matrix is an initiative to ensure all chat/messaging clients become interoperable. So, for example, if one person decides to use Telegram and another person Skype, they don't have to download each others software to have a conversation (just as you don't need to download Microsoft Outlook to send an email to someone who happens to use Microsoft Outlook.
So, you use riot.im on your iphone (or download any other program which allows you to connect to matrix). Once you're connected to matrix you can then create a 'bridge' between a room in matrix, or you as an individual, and a room in another chat service (or a direct connection to another user).
Those on the 'receiving end' do need to accept the bridge; but if you've got friends, a study group, a community group etc. using e.g. Telegram this will allow you to join and participate, it's pretty easy to setup and you only do it one time.
I don't think file sharing works (haven't tried it yet), but you can certainly chat.
IRC, Discord, Gitter, Slack, Skype and more.
Matrix is here: https://matrix.org/docs/projects/try-matrix-now.html
Happy to answer any other questions or help with tech setup etc.