Share a phone with a local audience

I would suggest using the right tool for the job.  A screwdriver can hammer a nail into a board, but it's not easy.  What you're asking is a scenario I believe few people would encounter and likely few solutions exist (IF ANY).

While presenting from a phone is possible - I've witnessed them - most people would connect the phone to a projector and provide the slide show that way (as was the case with the presentation I saw).  It would be possible to prevent "interruptions" from text messaging and the like by turning airplane mode on.  But preventing people in a meaningful way from "accidentally" advancing the slide... that's far less likely to be possible... especially since YOU have to be able to advance the slides at some point... I can only envision a possible way with a custom app only allows a "next" on the slides by, for example, holding down the "up" or "down" volume buttons or maybe holding one part of the screen and tapping another... I know of no programs that would do this and doubt they exist.

What you want to do is something I would not do. At the very least I'd do is if you want to do this is put your phone into airplane mode. A tablet would be a better alternative. I'd also be concerned about the security of the device.. Personally I'd never let the phone out of my physical control.  If I drop the phone and damage it, it is one thing, relying on others to handle it is something else. Use a tablet or a projector instead.