No, you cannot use the license code on a phone. The license code is for the desktop download software, which can only be used on a full PC or Mac that meets the system requirements for the download. It cannot be used on any sort of mobile device, nor can the license code be used to pay for the online software or the mobile app.
https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-mac-software/00/25609
If you do not have a computer that meets the system requirements, seek a refund for the download software, and then you can pay for and use the online software instead. But you have to pay the fees for the online software using another form of payment---you cannot pay with the license code.
To request a refund for a TT product
https://ttlc.intuit.com/turbotax-support/en-us/help-article/intuit-refunds/request-refund-turbotax-product/L834M6uyW_US_en_US?uid=m6meybc2