I have already purchased TargetScan in the Apple App Store, can I download it for free from Google Play (or other way round)?
No. You need to purchase the App again.
TargetScan is distributed through Apple App Store and Google Play. Those stores have your account information, credit card details and process payments. As a publisher I cannot identify you personally and cannot offer a licence for 'combined use'. Since both Apple and Google wants to lock you in their ecosystem it is unlikely they will offer such functionality in the future. So you need to use devices just from one company or pay twice for all Movies, Music, and Apps you purchase.
Also as a Developer I have to maintain two Apps: they share the name and concept, but the code is separate. So by buying the App on another platform you contribute to the cost of development.