H.W.
I'd say-- see if this lasts before talking to a specialist. If it has happened all of a sudden and only at consonant ends, it sounds to me like the teacher is over-emphasizing that part of the speech. So it could very well be a novelty. Plus, some kids go through short phases where their brain and mouth, as it were, are a little disconnected, so they'll hesitantly start a sentence with two or three words and repeat those until the whole thought/sentence 'gets there'.
And if you are asking him about it or commenting on it (even within his hearing) it will give the repeating of those consonant sounds more attention and make them MORE interesting to him. I haven't ever seen a true stutter just start suddenly... I'd talk to the teacher and ask to observe when she is teaching-- she may not even know she's over-emphasizing these sounds.
If they are teaching him a language which emphasizes the double consonant sounds of certain words, I'd say that it is likely imitative.