There are two images of Android on Dragonboard 410C.
Unfortunately both do not have playstore.
One is made by Qualcomm team which focusing to utilize the most feature out of the hardware.
This is suitable for just using Android out of the box on DragonBoard.
The other is made by Linaro (called Reference Platform Build) which is focusing using the latest effort of Linaro’s activities.
This is suitable for the developer who would like to enhance the AOSP on DragonBoard.
This is the link for the know issues.
So far, I am not aware of the 3rd party custom roms.