What type of chakra element does the Aburame clan possess?
I don't think it matters. The insects live under their skins in symbiosis with their host. The shinobi and the insects both benefit from this: the insects feed on their host's chakra (and I don't think they care about its type), and the host can use ninjutsu involving the insects. 

Note that ninjutsu must not necessarily be bound to a specific element. For example, Shadow Clone Technique is a ninjutsu which can be used by a lot of shinobi with different chakra types. Therefore, I think that Aburame clan members can have any chakra type.