If he can keep his head on straight I like his chances to be a top 20 WR next year.
Maybe I am missing something, but these alleged character issues have me scratching my head. The only issue I could find googling Burton is an incident with a Tennesse fan after the game. He admitted his mistake, apologized for it and has not repeated it.
The only other thing that people seem to be calling a "character" issue is his multiple transfers in HS and college. This feels overblown to me. Here is a video that parrots my perspective:
https://www.youtube.com/watch?v=ZK4x2H_tDo8
I looked into Burton a lot pre-combine and draft. The issues are more that no one had anything positive to say about him. Which coming into the combine and draft can be viewed as a flag in itself. Some bum who might not even get drafted will often get glowing reviews from former coaches, teachers, teammates, etc. "Hard worker, high intelligence, great locker room guy, lunch pail mentality" etc. etc. all that fluff. People want people they like to succeed and talk them up.
Not much of any of that happened for Burton. Reading between the lines, he rubbed everyone the wrong way and was likely just kind of a prick. People consider that a red flag. And the media needs something to talk about so it got insinuated it means he's "problematic" and has "character issues". Which could be 100% true. But, to me at least, you don't have to be nice to be good at your job.
In rookie drafts, and now in redrafts, I think his talent and his landing spot held against the fact he might be a jerk combined with his ADP make him a value. Considering his lack of off the field issues or things that could lead to actual suspensions and missing game time; I'm not overly concerned. And since the draft we've only really heard positive things from the Bengals. I'd imagine if he was still being an a-hole to everyone he meets we'd at least hear nothing. I wouldn't let the "character concerns" put you off on this guy IMO as it doesn't seem like anything beyond him not being a nice or likable guy. Most of Jordan's teammates thought he was a jerk too; sometimes that's just how uber-competitive people are. And again, his cost isn't so high that it really becomes much of a concern. He'll likely have to wait until Higgins is gone to really become fantasy relevant anyhow. Though I think if he shows out in preseason, his value will climb a bit.