There isn't a way to do this because you need to run data recovery software whilst your phone is in recovery mode. The data recovery software only work on a PC/Mac because the software needs the phone to be in recovery mode to run the commands it needs to to recover deleted file and configure them into the recognisable format.
There is no was to access recovery mode and deal with recovery of data on a phone at the same time on the same device or connected to another phone (if that even exists).
