You are permitted to advertise your text battles
HERE and your audio battles
HERE.
Basically, you can create a thread asking people to vote in your battles (include a link) but do not ask for them to vote for you specifically.
Being active in the forums would help because some people only feel inclined to check out the battles of people they know.
Having battles that place on the hotlist is probably what would help the most. With that, you'd have to consider who you're battling (battling higher ranked people and exclusive members increases your chances of being placed on the hotlist). Both you and your opponent would also have to be rated high by at least 5 people before hitting the hotlist (ranked between 8 and 10).
If you yourself are high in the monthly rankings, that also increases the likelihood of your battles hotlisting. Many people only read hotlist battles.