My little freaking degenerates, I love you.
There's some variables in the premise, so if we're ~*~asking questions~*~ these are the ones I'm starting with:
does Declan know Adam and Ronan are dating
does Declan know it's from Adam
does Declan know it's a sext
In all of these scenarios, btw, I am picturing Declan, after the confusion is cleared up, demanding to know how Adam could not tell which brother he was talking to from seeing the preceding texts in the thread, and then Adam has to admit that Ronan hates texting so much that Adam has actually texted with him less than he has texted with Declan. "Both of my Lynch threads with are just about needing a ride somewhere." "If you needing a ride so often means that I have to read about my brother's sex life, I will buy you a car myself." He's joking, obviously, but if he wasn't Adam thinks he would actually take the car. He's earned it.
If yes to all three questions, I think Declan deletes the first message and tries to ignore it (he is good at keeping secrets but bad at making peace with them). If there is more than one, then he sends a terse This is Declan. Change your contact names. They never speak of it to each other or to Ronan. Actually they don't speak to each other about anything for like half a year, Adam is too mortified. Anytime they end up in a room together it's just silence and averted eyes. Parrish ought to be better at subtlety than that; he would've given it away ages ago if this was anyone else they were dealing with, but Ronan has very large blind spots, especially where his family is concerned. He tends to miss things that don't fit with what he's already convinced himself is the truth. For once Declan is grateful.
If Declan doesn't know Adam and Ronan are dating then I think yeah, he rolls with it: huh, I wouldn't have considered Parrish, but if he's putting himself out there, sure, I'll bite. Under those conditions he isn't going to notice anything's wrong, especially if Adam calls him "Lynch" at some point. So it's entirely up to Adam in this scenario to realize his mistake, and that means the reaction is entirely up to Adam, at least to start. Would he end things with an abrupt "I take it back, let's not do this anymore" and not tell Declan he was a misdial? That preserves the secrecy, if that's a priority for either him or Ronan or both, and it's less embarrassing in the immediate moment. But it does leave him worrying, crap, Declan thinks I'm into him, what if he says something, what if he does something, what is he going to think when he finds out about us and realizes I was sexting someone else while I was dating his brother. So I think he would bite the bullet and admit to Declan that he'd made a mistake; maybe he wouldn't specify who it WAS meant for, although I think Declan would put it together pretty easily (especially if Adam did call him Lynch), so that would not last very long. In this situation I think that they do tell Ronan (specifically, Adam tells Ronan), because Adam feels like Ronan deserves to know that Declan knows they're together. He does debate for a bit on whether to tell Ronan the full story, would it really be thaaaat bad to just let Ronan think that Adam outted him for no reason, but he knows he has to tell him the whole truth. Ronan for sure has some initial blow up at Declan, but I'm torn on how he handles it in the long run. "Wants to just pretend it never happened" is good, but "frequently brings it up to shame Declan and uses the fact that Declan 1. sexts and 2. finds Adam attractive as proof of some moral failing on Declan's part, while never acknowledges the hypocrisy that he himself does both of these things" is also very good.
If Declan doesn't know it's Adam -- let's say he has a new phone and lost his contacts. One day some number he doesn't know just sends him a flirty message out of the blue. He assumes it's someone he hooked up with in the past, because who else would it be? He plays along, because why not have a little more fun with someone he must have liked fine before, and also why admit hey I don't know who this is when he can probably figure it out eventually. (Yes I do realize I have written the non-sexual version of this scenario before, "Declan refusing to admit he doesn't know what's happening so he just goes along with it so he can figure it out along the way without exposing any weakness" is a good scenario.) The problem with this one is that I cannot decide when & how the mix up is discovered. I kinda want it to be never; that doesn't feel terribly plausible (either of them could see the messages in the thread the next time they intentionally text each other), but I am cracking up at the idea that Adam thinks it was Ronan and Declan thinks it was a last flirtation with some old flame. It never happens again, they both just have these different memories of the same event for the rest of their lives.
If Declan doesn't (at first) know its a sext -- this one depends on the "what kind of sexter is Adam," question. I think he'd probably start off playful and flirty instead of just opening with I wanna X your Y. (I definitely think that Adam doesn’t send dirty pictures over text message -- too cautious for that -- and I don’t see the two of them being friends on Snapchat/whatever the kids are using for nudes these days.) Without the right context, and without visual cues or tone of voice to go off of, it's more likely that Declan would misinterpret it than that he would immediately assume it was a prelude to something dirty. To go with a PAINFULLY cliche example, if Adam texts him "what are you wearing," Declan is probably going to wonder why does Parrish need to know that, is he trying to find me in a crowd, so then his response is going to just be like "why, are you coming to visit" but Adam ALSO does not have the right context or visual cues or tone of voice, so HE'S going to misinterpret that as engagement with the whole sexting premise. So now he messages back, you tell me, are you lonely and Declan has a fucking existential crisis, because yes he always at all times in all places is lonely but why is Parrish just dropping that question on him, how did he notice, why is he challenging him about it. He realizes what's happening when the flirting/sexting becomes overt, and as awkward and embarrassing as that is it's also kind of a relief, oh okay Parrish is not staring past my armor and into my soul, he's just careless and horny, except it's also not a relief because for a second he felt slightly less alone and now the second is over