Do they ever get flagged as junk messages, and is there a way around that? (E.g. having the participants enter in the phone number where texts are coming from as a known contact)
FollowWe can't guarantee that mobile carriers won't flag something as spam, but we encourage you not to put things like "take this survey and earn $!" or anything that looks "spammy." Also, the respondents replying to the messages shows the carrier that they actually want to receive them and are interacting.
Having participants enter the number as a known contact won't matter to the mobile carrier (they can't see our contacts), but it will let the participant know it's coming from your study, so it's a good idea to set them up that way!