http://iscoresports.com/

I purchased and use the app from the Google Play Market. Recently got an Amazon Kindle. Is there any way to get a copy for the Kindle without having to buy a new one?

Amazon does not allow installing the Google Play Market. They want everyone with Kindle to purchase through the Amazon App Store. If they ever allow installing the Google Play Market, then you would not need to purchase again, but for now, there is no other option.

If I pay for it, can both accounts be joined so that I can use either device and they will all stay synced?

You can use Data Sharing to transfer data between devices. Here is a link that describes data sharing:

http://iscoresports.com/baseball/kb/faq ... _share.php