Lonnnng time lurker.. First post.
Chase has lots of problems with their public landing pages, incl. their main banking page. And (probably because of FT users!) the Chase gift card purchase main page bogs down.
Anyway, skip the main public link (from post #1), and go straight to the secure gift card purchase page:
https://www.chasewebgiftpurchase.com/index.cfm
Also, once you're on the page with your cart loaded up with GCs, if the main "Checkout" button doesn't work for you, try the Checkout link way up at the tip-top of the page (next to "View Cart").