Like Barry Allen in Crisis on Infinite Earths, he appears to Batman to deliver a warning that is also a cry for help that Batman is unable to satisfy.
Like Barry Allen in Flashpoint, he comes to Batman to deliver a message about reality having changed. The status as a messenger is, in turn, a reference to the Roman god Mercury, who also inspired the first Flash, Jay Garrick.
Like Barry Allen in 2008's Final Crisis one-shot lead-in DC Universe #0, he is the narrator, initially unidentified, with yellow-and-red narration boxes as a clue to his identity before it is revealed.
Like Barry Allen in Flash Rebirth, he is lost in the Speed Force, seeking an anchor to pull him back to reality.
Like Barry Allen in Final Crisis, he gets back to reality, and then participates in an emotional reunion with his former partner.
Like himself – Wally West – in a JLA-JSA crossover called "The Lightning Saga" he returns to continuity after a prolonged duration in which his absence was a creative decision by DC that was eventually reversed.
But he is also playing the roles of two non-Flashes: Like Doctor Manhattan (on two occasions) in Watchmen, he is nearly blown apart by cosmic forces, but survives to return to reality. As with several of the correspondences mentioned above, the artwork is intentionally composed to remind us of the connection, but in the case of Watchmen, it is a clue (of several) pointing to a further reveal that Watchmen's universe is connected to the DC Universe.
Like Johnny Thunder, he is a bearer of lightning. Johnny's appearance as an old man is used early in Rebirth to let us know that the Justice Society was always part of the post-Flashpoint history, but it was hidden and forgotten.
And, like Geoff Johns, the writer of Rebirth, Wally West is telling us how he feels about the DC Universe: "I look down at it and know without question: I love this world." Johns certainly does love the DC Universe, and Rebirth is a love letter to many things that it has been, and, as Rebirth tells us, manifesto-style, will soon be again. This applies to all of the scenes I've so far mentioned and many more, including the conversation between Superman and Destiny and the mysterious appearance of a Legionnaire, probably Saturn Girl (Legionnaires fulfilling a mysterious mission in the present was also part of the aforementioned "Lightning Saga").
Geoff Johns, presenting DC, is bringing things back, and he's excited about them. There's a lot to love. I'm excited about some of it, and other readers will be excited by a lot of it, too.
Where my enthusiasm grows dim, and where many of the aforementioned references to previous changes in continuity fail, is that what DC's creators brought back now are things that they themselves discarded in the very recent past. This is not a twenty-year rebirth, reversing the decisions of departed former bosses. Jenette Kahn, the longtime DC publisher whose tenure killed off Barry Allen, Hal Jordan, and the Multiverse, left DC in 2002; Johns and his new bosses began reversing those creative changes almost at once. But this time around isn't a revolution (or counter-revolution) under new bosses. This time, the Powers-That-Be are the same Powers-That-Were when all of the changes that are being reversed were made in the first place. Johns, et al made the creative decision to pare down DC Continuity in 2011 believing that those changes were good. Now, they undo those decisions, believing that it is good to undo them.
I was greatly enthusiastic about many of the changes made in 2011, and greatly disappointed in the lack of inspiration shown by many of the writers who wrote 2011's new titles. Some of 2016's changes, I regret. Others, I look forward to. But the key, as now, is not those changes, but whether or not DC has a stable of writers ready to write great stories. Revisiting the past can be a wonderful thing, and it can be done wonderfully. But if DC will be revisiting not only the facts and style points of the past, but also the same general plots and same general kinds of stories that we've already seen, my enthusiasm – and that of other readers – will dim in 2017 just as it did in 2012. I believe that any writer who can't make the New 52 exciting can't make the Rebirth era exciting, either. The creative direction changes nothing in that regard, and so the burden is on DC to show that change is good change, and not simply recycling.
"Nothing ever ends," quoted from Watchmen, is the last line of Rebirth. How DC approaches the new beginning will determine if we should interpret that line as a promise or a threat.