Say if you work at company A, and you sometimes and currently work in partnership with company B. Company B is also a competitor at some times, but rarely.

Would it be appropriate to contact someone you know at company B (because you are working with them), and asking if they have any open job positions?

I want to work at B, I have tried applying online but they are HUGE and I feel the bureaucracy is preventing the right people from see my resume.

What do you guys think?

If you know the right person, sure why not.

As long as you don't have a non-competition clause in your current employment contract, I say go for it.

Umm... there are two issues here:

#1 Can you legally do this:

Say if you work at company A, and you sometimes and currently work in partnership with company B.

You may have already violated your contract. Some contracts even say you can't work for a competitor within so many months of quitting, I believe (but those are pretty draconian).

Aside from that...

#2:

Would it be appropriate to contact someone you know at company B (because you are working with them), and asking if they have any open job positions?

You mean the ethical ramifications of using a social/political connection to get a job?

You have an advantage- use it!
If you don't use a connection you have, that's not so much an ethical question, as one of sanity

Best of luck!

As long as you don't have a non-competition clause in your current employment contract, I say go for it.

Unless you are in California, where non-compete clauses don't mean anything, because they are not legally binding.