According to the most official source we have in English, the dictionary, both pronunciations are valid.
The pronunciation of a borrowed word in the originating language has no bearing on the "proper" pronunciation of the word in English. However, the word conch comes from Latin concha, which would have been pronounced /konkʰa/ in Latin (to my knowledge). The raised "h" represents an aspirated /k/ sound, and it is different from both of the /tʃ/ and /k/ sounds suggested in the dictionary. As it happens, we also sometimes have an aspirated-k (kʰ) in English — however, we do it word-initially and in stressed syllables (only), and never in non-word-initial unstressed syllables. So, the unaspirated-k at the beginning of that word and the aspirated-k in the second syllable are reversed with respect to the natural English pronunciation (i.e. /kʰonka/ would follow English aspiration rules), and so pronouncing the word in the Latin way would sound quite odd mixed in with normal English speech.