They are both possible. The subject of the sentence is "His charm and the fact that he is so likeable". You could consider these to be two separate factors and use 'allow', or you could consider them to be a single element (a combination of these factors) and use 'allows'. My preference would be for the latter. This is because the idea of charm and likeability are essentially the same thing - it is basically just one idea. NB The fact that you are talking about one person rather than several is obviously irrelevant.

We are talking about a single person, he, in this sentence. To ensure subject-verb agreement, we should use the word allows. "His charm and the fact that he is so likeable often allows him to get away with murder." If there were multiple people involved, for example, "they", then we would have used "allow". Hope this helps!