The following contains spoilers for The Flash #786, on sale now from DC Comics.
Wally West has a perfect life right now. After being erased from existence by Flashpoint and brought back to a broken life in DC Rebirth, the past few years have been tough on him. However, after his full history was restored after Dark Nights: Death Metal, he got his family back. He also reclaimed the mantel he was born for - the mantel of the Flash.
Even with this new happy-go-lucky lease on life, Wally has apparently been hiding something. The Flash #786 (by Jeremy Adams, Amancay Nahuelpan, Jeromy Cox, Peter Pantazis, and AW's Justin Burch) was a Dark Crisis tie-in that saw Wally and the rest of the Flash Family go up against a whole host of villains, spurred on by the encroaching Crisis. One of these villains was Klarion the Witch Boy, and he had something very interesting to reveal about Wally.
Klarion talked about how the world had been ordered, and how Wally apparently knew all about it. The reason for that was the Mobius Chair. Having sat in the Mobius Chair and seen all of its knowledge, Wally apparently knows a lot more about the bigger picture than most people do. Klarion mentioned the Great Darkness, who is the apparent villain of Dark Crisis, but then also talked about something going on with Hypertime. This most likely alludes to the other Crisis going on in the pages of Flashpoint Beyond at the minute. Despite not sitting on the chair anymore, Wally apparently knows all of it.
Wally West first sat on the Mobius Chair in the wake of Heroes in Crisis. After his involvement in the accidental deaths of the heroes at Sanctuary, Wally was recruited on a mission of multiversal redemption. After removing all the invading Dark Matter from the multiverse, Wally managed to save his kids from certain doom - but only by sitting on the Mobius Chair. The powerful artifact having also been imbued with the power of Dr. Manhattan, the Chair allowed him to see reality for what it was, on top of the Chair's almost limitless knowledge. Wally was omnipotent and even had plans to fix all the decades of damage inflicted on reality all by himself.
Wally isn't the only mortal to have sat in the Mobius Chair. In fact, he isn't even the only Justice League member to do so. During the "Darkseid War" in the New 52 Justice League, Batman sat in the Chair. It was actually how he first learned of the three Jokers. Of course, it changed him while he sat on it, and he gave it up. Since then, he's gone back to being the same Dark Knight he's always been, with no mention of any lingering effects from the chair. The only thing of note is his investigation into the three Jokers. However, it's worth bearing in mind that when Wally sat on the Chair, it was imbued with the energy of Dr. Manhattan too. No other individual has sat on the chair when it had that power. At least, no one still living anyway.
That fact may alter how the Mobius Chair affected Wally. It would explain why Klarion suggested he was aware of what was going on with Hypertime and with the Great Darkness even now. From that comment alone, it's clear that Wally hides how much the Mobius Chair affected him and what his true view of reality really is. It has been noted that he's been different since the universal reset of Death Metal. This was mainly attributed to the fact that he got his family back. Whilst that's sure to be a major factor, it may be that his view of the whole universe is different too.
When it comes down to it, Wally West has been hiding something from everyone - even his family. He no longer sits on the Mobius Chair though so, really, he doesn't have access to that vast, mind-blowing amount of knowledge. However, he's clearly aware of the broader strokes of the universe and the cosmic turmoil brewing in the background. This suggests that, to some extent, Wally only pretends to be a regular, family-man superhero. He loves his family, of course, but that's why he hides what he really knows about the DC Universe.