It varies by a lot.
In most cases, you need to be approved by the FBO to instruct. It protects the FBO and is probably required by insurance.
Once getting over that hurdle, whether an FBO will let you depends on a number of factors. In some cases the insurance that covers the FBO for problems caused by CFIs has limits on the number of CFIs that the FBO can use.
Beyond that, is a matter of their own business policies. CFIs are connected with FBOs as either employees or independent contractors. FBOs use one or the other model or a combination of both. Sometimes the model is geographic — most flight school in the same area may follow the same model.
Best is to select a few FBOs and ask. If you're truly looking freelance, make sure you let them know that you're looking for a place to =bring= students, not a place to =find= students. That can make a big difference!