Among the five basic elements of chakra (earth, water, wind, lightning and fire), what type of chakra does the Aburame clan possess to control insects at their will?
It very well could be a Kekkai Genkai, a ninja ability that is genetic or passed down by nature genetically, i.e. Bakugan, or Shadow Weaving (the Nara Clan). The make up of these abilities is not known and is really a family secret only known to those within the clan.
Chakra is based on In (Yin) and Yo (Yang). If both come together, Seishitsuhenka can be applied to the chakra. Some techniques (like Kagebunshin no jutsu) only work with manipulating In and Yo (only if both are combined 1:1, the "normal" chakra(like used in Rasengan) is created). Because Kikaichū no Jutsu and the other Jutsus needs no signs, no chakra is manipulated. They are only simple techniques to be used with the knowledge of insects.
All in all, it's never shown that members of the Aburame-clan don't use Seishitsuhenka.
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.