I tested this with Walkthrough from MDN. I ran Firefox 48.0, releasing a version. This answer assumes xpinstall.signatures.required set to false in about:config .
The add-in is not installed if you go directly to file:/// URL:
It seems that Firefox has disabled the installation of unsigned extensions by directly clicking on the file:/// link (I have not tested signed extensions yet). Thus, using the adb shell am start -a android.intent.action.VIEW method adb shell am start -a android.intent.action.VIEW using the intent to force Firefox to go to the file:///mnt/sdcard/extentionFile.xpi will only result in a "Blocked Add-on" dialog, without the possibility allow, from which you included a screenshot in your question. This dialog is the same if you manually enter the URL.
You can install the add-in without signing:
You can download the unsigned extension by going to Firefox to the directory containing the .xpi file (for example, file: /// mnt / sdcard / ), then click / tap on the file.
Thus, for adb you will need to open the directory, and not try to open Firefox directly. The adb command you want to use depending on your question will be:
adb shell am start -a android.intent.action.VIEW -c android.intent.category.DEFAULT -d file:///mnt/sdcard/ -n $ANDROID_APP_ID/.App;
On your phone you will need to select the file $APP_NAME.xpi . You will be presented with one or more screens through which you can click to install the add-on.
These are the screens that I shot during testing. To have an empty directory, I used /mnt/sdcard/testing/ instead of /mnt/sdcard/ .
Firstly, I used adb to navigate to the directory in Firefox (this is for convenience, you can access it through the phone’s user interface) using the command:
adb" shell am start -a android.intent.action.VIEW -c android.intent.category.DEFAULT -d file:///mnt/sdcard/testing/ -n org.mozilla.firefox/.App
This causes Firefox to open the directory ( file:///mnt/sdcard/testing/ ):

Press / select the .xpi file. In this case, it is view-source.xpi.
The Blocked Add-on dialog box appears. This dialog box will have the “Allow” installation option. You can skip this dialog by setting xpinstall.whitelist.required to false in about:config . But this still will not allow you to install by directly navigating the file using the intent or entering it into the Firefox user interface]:

Then a dialog box will appear asking if you want to install an unverified add-on:

After that, the installation is performed:
