Is it possible to get a civil partnership application from the US embassy in the philippines?
No, because the USA does not have civil partnerships. Civil partnerships are, however, the same thing as gay marriage. Gay marriage is legal in a very few US states but it is not legal at the federal level. A K-1 visa is similar, though – it allows you to go to the USA to be married there but of course the marriage has to be possible in the state you are going to, and in most of the USA gay marriage is not possible. So unless the person you want to marry lives in one of the states where gay marriage is possible, the answer to your question is no.