How to stitch together MFCCs from multiple frames?
How should I combine these groups of 12 coefficients to get some
  value(s) that describe the whole signal?


I don't think "flattening" the sequence of $215 \times 12$ coefficients into a $1 \times N$ vector, and then computing the distance between these vectors to compare two sounds is a good idea. This approach collapses the temporal information - the way a sound evolves in time. For example, let us say that you decide to use the standard deviation and mean of each coefficient to "summarize" the sequence of MFCC vectors (this is a technique used in some applications). If you use this approach, both a sound and the same sound played backwards will yield exactly the same feature vector! This might work for simple tasks like recognizing different music instruments, but as soon as the temporal information needs to be preserved (distinguishing "halo" and "hola", or a drum instrument playing "boom boom tchik" vs "boom tchik boom"), thinking in terms of vectors rather than sequences no longer works.

This might not be the answer you expect, but I suggest you to stop reasoning in terms of vector comparison, and rather think of a way of comparing the sequences of MFCC frames themselves. Your approach - which is akin to computing the raw pairwise distance between sequence of vectors - is not robust to difference in timing between the two sequences. The solution is to use Dynamic Time Warping. It attempts to optimally align the two sequences in time (so that comparing "hoooolaa   " with "   holaaa" yields the same score as comparing "hola" and "hola"). This technique is good enough for basic voice command recognition.

Another approach would be to model each sound by a HMM with a few states; and to use the distance between models as a similarity metric. This can be more computationally efficient, and put you in control of how strict you want to respect temporal information (by increasing the number of states).