I am currently part of an LLC in which we all bought a house in order to flip it. The flip did not go well and now we are going to hold it as rental investment. Unfortunately, the mortgage is at 11% APR via a hard money lender and we want to refinance to a lower APR. I have offered the group that I can refinance the home in my name and lend them (the LLC, that I'm also a part of) the money at 8% APR. Can I do this and if so what do I need to do to establish this contractual agreement? How I do I run the numbers to see if this is a good deal for me?

You can typically refinance investment property at about 4.3 to 4.8%. There's plenty of room in your 8% offer to make money on the spread. That's a no brainer. 

You would have to document this separately from the properties recorded documents. You would have to simply create a finance agreement and a promissory note for each partner. You're protected already by your name being on the deeds when you refinance. Additionally a signed and notarized promissory note will give you leverage to collect if necessary. 

You can look into a wrap mortgage (all inclusive trust deed); or you can simply put the property into a land trust after you refinance with the equity of each partner spelled out in the trust. 

lots of options. Hopefully more people chime in.