I'd say do it by hand. First write down all 214 Putonghua phonemes and convert them to symbol tokens in your universal phonetic alphabet. Now write down all N English phonemes and convert them to symbol tokens in the universal phonetic alphabet. Write it so it's two columns, and if the same symbol is used in the universal phonetic alphabet, then they are shared. That's how you do the first part.
Now for the second part, set up a correspondence between your 214 phonemes and their equivalents in pinyin, then take a largish sized representative Putonghua corpus (a million characters or so should work), convert it to pinyin, then convert it to your 214-phoneme system, then tokenize it. Now cross out all of the ones which were counted as "shared" in part I. Now rank them by decreasing token frequency.
That's it! The only tricky part is in deciding on your universal phonetic alphabet, or put another way, what counts as "the same thing" between English and Putonghua.