Is failing to delete a video within 10 seconds due to a phone malfunction considered breaking an oath, given that the oath was to delete it within that timeframe?

If your brother was unable to delete the picture due to a defect beyond his control, then the preponderant opinion is that you have not broken your oath. Similarly, an oath is not broken in cases of duress or inability, whether the inability is due to a شرعي ( Shar'i - religiously lawful) impediment or a كوني قدري (kawni qadari - divinely decreed cosmic) one. Likewise, whoever swears to do something but is prevented from doing it, is not considered to have broken his oath.