Sure you can use flat-leaf parsley instead of cilantro - but it will change the flavor .... but then you obviously already knew that since you wanted to sub something for the cilantro. I'm also not a big fan of cilantro - but in this case it is a flavor component - maybe use 1/2 cilantro and 1/2 parsley?
One thing I would suggest - if your going to use the marinade as a sauce to put on the finished dish .... put it in a sauce pan, bring it to a boil for 1 minute, then simmer for at least 3 minutes. Remember, this has been in contact with raw meat .... that you are now going to pour over cooked meat. If you "cook" the marinade then you'll get rid of any nasty little "bugs" picked up from the raw meat.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain