No you cannot download the CD/download to any sort of mobile device--- only to a full PC or Mac. If you only have a mobile device you can use the web-based online software. Not sure if even that can be done on a Kindle.
Where did you purchase the software?
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-mac-software/00/25609
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-windows-software/00/26175