Unfortunately there isn't a Snapchat app for Windows phone at the moment. And there isn't really a way to access your Snapchat account via Windows phone anymore either... which is actually more the fault of Snapchat than Windows. Let me explain:
There were several apps for the Windows phone that allowed you to access your Snapchat account, but they were third party apps, and Snapchat decided this was breaching their terms (and was a potential security risk, which is in fairness is a good reason for being cautious).
Keep in mind that there was a serious Snapchat hack in 2014 where millions of accounts had passwords and other data exposed. You can understand why Snapchat might not be too keen on third party apps plugging into their app.
Snapchat therefore decided that anyone using a third party app to access the platform would have their accounts locked. They warned people but then went ahead and followed through on their threat.
In the past few days they have gone a step further and demanded that all third party Snapchat apps are removed from the app stores.
This obviously means that Snapchat are aware that they have a whole host of people who want to use the app but are unable to, so hopefully they will now release the app for Windows phone which, to be honest, I can't see why they haven't already done!
Windows phone is a very popular platform, Snapchat is a very popular app so it makes sense to make sure that it is available to these people too.
