My wife was instantly approved for the Arrival card on Monday. Already had Barclay US Airways, approved 7 months ago (3k limit - was acquired while bankruptcy still showing, has since fallen off).
I'm now convinced that the key to Barclay's instant approvals is two fold:
1) Must be 6 months after any other successful Barclay's card app.
2) Must reduce credit limit to well below what they are willing to offer you overall.
I've now had success myself and my wife with those two rules, and several denials when I didn't follow those rules myself.