How long will it take to upgrade the speed of my Azure primary and secondary connections?

It shouldn't take long., typically less than 5 min. Exceptions to this would be if there is a capacity limitation. Please note, the connection speed is determined by the ExpressRoute key.

 A few additional notes can be found below:

Traffic continues to flow at the previous lower speed when the bandwidth upgrade is being configured until the upgrade on both the A-side and Z-side of the circuit is successfully completed.

Increase Azure ExpressRoute Bandwidth

Create and Modify an ExpressRoute Circuit.