My daughter purchased it from play store. but as her Android phone went phizz phiz plop, she has now got W81 phone.
She now uses my Android tablet and would like to now if there is a way for her to transfer purchase to my play store account, to continue usoing her Chromecast, which probably killed her phone 
You would need to sign into the account that you purchased the application with on the tablet. By that I mean, if you all used her account to purchase it, she will need to sign into her account for the PlayStore (under Settings, Accounts, Add Account, Google) on the tablet. After this, you should be able to re-download the app since it is already paid for.
Only down side is you will have her account on your tablet. Just make sure you turn off backups, emails, etc. to and from that account to avoid any cross contamination with her information as opposed to your stuff. 
:))
You cannot transfer purchases to other accounts with Google Play.
However if you are only using the Chromecast to actually watch things, you do not need to purchase the app. The activation only enables playing on the tablet/device itself from a server. You can cast to a chromecast at no charge.
Your daughter only need to sign into he Plex account in the app to view her media list. > connect to the chromecast > hit play on the thing she want to view > it starts playing on the chromecast
