Barry will likely never get in the pro HOF. Just like Trent Dilfer will never get in, despite being a Super Bowl winning quarterback. The converntional wisdom in the NFL, (sounds like an oxymoron) is that Jimmy Johnson built that team. Few Cowboy star players thought that Barry was a good pro coach. Their view is mostly that the Cowboys won the Super Bowl despite Barry, not because of him. He might get in 20 years after he's gone (not from coaching, but from life) but pro football doesn;t hold Barry in high esteem, and certainly not in Hall of Fame esteem.
To get in the Hall in pro football, you have to have at least one media member to carry the ball for you. There is nobody I know of in football journalism who has a super urge to carry Barry's water. Without that, he won't sniff the Pro Football HoF.