I've been asked frequently from my writer and artists friends how to get published. I can honestly say there is no right way to do it. I submit a piece 20-30 times through various literary journals before I get any feedback whatsoever let alone an acceptance. My fiction does not fit the archetype of traditional publishing, so fitting my work with the right publication is a process. To all who ask I just say: keep submitting. Your piece isn't going to get published in your first, fifth, or maybe even hundredth submission. That's how publishing works, it's much more beneficial finding the right outlet to publish your work versus giving up. Naming the Stars was rejected countless times before I found a call for submissions that fit the theme of diaspora.
The editing process is another big problem within publication. Most journals aren't going to sit and comb through your piece for line edits or plot holes. Your piece needs to be publishing ready the second you turn it in. If its a matter of your grammatical differences moving away from a magazine or a journal that has strict grammatical requirements may be necessary. I use grammar in my style of writing and play with it constantly and I've been rejected because of it.
Finding the publication that is going to work for you and your piece is key. Being rejected is a part of the journey of a writer and just because you were rejected should not discourage you from submitting or writing.