Currently only a new message can be used as a trigger. A reply to a message also needs to be added so that any type of message added to a channel can be used to trigger an action.
Actually current behavior of the new message trigger looks like a bug or unfinished feature. In response metadata and attributes of the trigger there is "replyToId" field, but indeed flow doesn't start from replies to message, only when new thread is started.
I have same problem.
Hence users refrain from using teams as they are not nofified is someone replies to a conversation.
Only get e-mail if they started the converstation.
Unless I'm missing something, I think this is now possible. See v-bacao-msft's solution here:https://powerusers.microsoft.com/t5/Building-Flows/Dynamic-content-not-supprted-for-Microsoft-Teams-...
Going by v-bacao-msft's second reply it doesnt look like it applies to replies."Unfortunately, the action in Teams connector is currently unable to pull message replies from a message in the teams channel."
Have to say I'm might miffed. Got a great flow setup to enable a conversation interaction only to find out that flow can't process any of the replies.
This surely is an oversight. Having reply seems a basic need, especially given Teams is naturally threaded