That is awesome that you have a heart to help children, but working with homeschool families may prove to be too narrow to be successful. If you are, or have been a homeschool parent, that should help you establish a connection, but it sounds like your moving? If you're new, it will be difficult.
If you are not a homeschool parent, are you a certified teacher? That would give you an opportunity to work with the local school district. I know the schools are always needing a list of names of people that are willing to tutor, but again, you would have to be certified (even retired is ok) and you would have to basically be an employee, submitting to background checks and so forth.
If neither of those describe you, then connect with a library or rec center. You can register as a volunteer, submit yourself to their reference checks and background checks then establish yourself as a homework helps person. Our rec center offers homework help, but most of the time they don't have anyone willing to work with the kids. After school, our particular library is full of students waiting for their parents to get off work (free babysitting.) They may be willing to set something up with you to use one of their rooms to tutor. Any of those options would require more than just printing up flyers and such. you would need to establish a good relationship with your librarian or rec center director. They can be your best friend in directing potential clients your way.
homeschool group director, two years.
worked very closely with our librarian and rec center director