He doesn't appear in the final chapter of Bleach but that shouldn't necessarily mean he's dead, right?
The official status of Urahara is Unconfirmed. While the evidence seems to indicate that he died with Yoruichi and Grimmjow trapped in Askin's Gift Ball, Kubo also gave them a way out. Nel was watching the battle from outside and later decides to attempt a rescue attempt.
Wiki sums this up pretty nicely, but this is the last we see of these characters.
After being impaled once more by Grimmjow, who suddenly buckles alongside Urahara, Askin reveals that the power of his Gift Ball Deluxe magnifies upon his death. As Askin decides to forgo the speech about lethality, Urahara and his Bankai collapse as Urahara apologizes for leaving everything to Ichigo Kurosaki and Rukia Kuchiki
Nelliel later stands outside Askin Nakk Le Vaar's Gift Bereich, noting how it is collapsing like Urahara thought it might. She remarks that carrying four souls out of it would be difficult, and is shocked to see that the entrance is so small. She remarks that she wanted to see Ichigo again as she leaps toward the entrance.
Kubo can also put these details in a databook later. I have seen that Bleach rarely kills characters if they can be "brought back" from the brink of death, so Urahara and others have a good chance of still being Alive.