I'd suggest setting up a ipv6 only network (you'll need an ipv6 router and a DNS server - more if you want to test across subnets). Dual Stack can be a challenge to test, as fallback to v4 may mask v6 issues. An app (assuming it uses the network) should behave the same running on ipv4 or ipv6 networks.
You can also simply review the code to see if/where ip address are manipulated, or if if ther are low level socket commands that could cause a problem. If the networking calls are all high level (or non-protocol specific), you shouldn't have (m)any problems.
If you need to test ipv6 interet traffic, ipv6.com has several resources that should help (also search 'ipv6 tunnel broker' if you need to ensure ipv6 only traffic).