Does the IR Blaster on an Android phone receive as well as send? Is the IR Blaster communication two-way or only one-way? I have seen many remote control apps for my Android phone but none that learn from an existing remote.
For transmitting, a single Infrared LED and resistor are needed. For receiving, an IR receiver module with internal bandpass filter is needed.

There are remotes that will send and receive. Universal remotes will sometimes have a "learning mode" to mimic another remote.  An example of this at the bottom of my answer.

But a receiving IR isn't a standard feature on Android devices, as of this answer I haven't heard of or have found any online of that can. But with a PC program and Android app you can mimic remotes. The link below is one such program.

Unified Remote. There is a free version and a paid version with more features. 

The link is just for the feature list of the app. There is a server (PC) side as well as Android side.The amount of remotes that you can map over to your device is staggering, I think you can even design your own remotes. By using one of the remote templates, your device is effectively "learning/receiving" the other remotes codes (you don't even have to have another remote physically there). You would still be accomplishing your goal.



example

I had a Yamaha Natural Sound home theater receiver and the remote had a "Learn Mode". So you switch it to learn, place the "other" remote in front of it. Press the button on "other" remote, then press a button on the Yamaha remote that you want that command mapped to. You now have control of the other devices functions. You can also clear mapped button commands and enter new ones as needed.