I’ve been able to add my washer and dryer to SmartThings on my phone, and when they finished their cycles I get a notification letting me know.
Is there a way I can have this notification announced via my Amazon Alexa? I don’t have a SmartThings hub, just the app on my phone.
I’m pretty new to the whole smart home world, and I don’t know if this is something that I’m missing, or even possible.
3y later, you still got no reply, and I am looking for the same thing 
I don’t think you can do this without a hub, but if you can add the SmartThings skill to the Alexa app, and if it detects the washer and dryer as devices, then you should be able to do this by using an Alexa routine that uses Alexa’s “Announce” function.
I was able to link the accounts (via skill), and the washer and dryer are visible as devices.
But when I am creating a routine, and selecting the “when” trigger, if I choose “smart device” it only shows Amazon devices, and none of the others (washer, dryer, lights, blinds, etc.) 
I wonder if it might take some time for those to come over? Or maybe if you remove those devices from the SmartThings app and re-add them Alexa will then detect them?
You can also try to create a virtual switch in SmartThings that Alexa can see, then turn on that virtual switch in a SmartThings routine when your washer is done, and do an Alexa announcement when it detects that the virtual switch has been turned on. It might be a little tricky to set that up if you’ve never done it before, but here’s a link that talks about it:
The OP said they don’t have a SmartThings hub, and VEdge Creator, like all edge drivers, does require a SmartThings/Aeotec hub, since that’s where edge drivers run.
That said, the basic idea is sound: whether you have a SmartThings hub or not, you can use some virtual devices as the trigger for an Alexa routine (not a SmartThings routine) and then use that to get Alexa to make an announcement. This is a very popular use case, whether you have a ST hub or not.
So good suggestion, it’s just that the details of how to do it are going to be different for those who don’t have a hub.
The community FAQ on getting Alexa to do something covers both configurations, so it should explain:
FAQ: Can I trigger an Echo Action without Speaking to It?
also, the reason that only a few devices show up as possible triggers for an Alexa routine is because of a limitation on the Alexa side. Only some sensors, locks, doorbells, and a few specific buttons will work. Other device classes don’t work.
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And definitely don’t delete anything from your account and re-add them: there are some platform issues right now, and you may have a very hard time adding them back. Plus at the time of this posting it’s not going to make any difference anyway. Those device classes just don’t work as Alexa routine triggers.
Ah, cool. I’m glad someone with more knowledge about this than me chimed in! Thanks, JD!