No, not only word-initial though it does seem that it's almost always syllable-initial.
There are many examples, assembled at 'a cross linguistic lexicon of the labial flap' by Olson and Hajek.
Most of the O&H examples show it occurring in word-initial or intervocalic position, but there is at least one example of it in a consonant cluster (tho heterosyllabic), from Karang (Niger-Congo, Cameroon):
/pekⱱekⱱek/ ‘very high’
There is also a single example in the O&H dataset of a word-final occurrence, from Dii (Niger-Congo, Cameroon):
/ɓáⱱ/ 'sound of a horse galloping'