Is there a conflict of interest between me and the university if I get paid on teaching others how to apply for the PhD positions in my university?
Three thoughts:

(1) It's hard to see how this is a conflict of interest if you have no role (even informally) in the admissions process. 

(2) Writing an applicant's personal statement for them is unethical. If you are advising students on the best strategies for dealing with particular individuals in your department, that also seems a bit like "insider information."

(3) You should consider the (not so remote) possibility that your department will become aware of your role on this platform. If you are okay with this, then it is likely ethical. You may even want to consider discussing it proactively with a trusted professor (e.g., the graduate program director).