I've worked for a couple of SAT prep companies but they are smaller/more local in the Boston area and I tutor (don't teach) Both wanted to know my SAT scores from high school, and one made me retake the SAT with them to show I can still score high. I think they are looking for mid-700s on each. I think Kaplan makes you come in and do a teaching audition for the classes- I looked into it during college.
You might want to look into tutoring too. I have education experience so it was not hard for me to get the jobs but they do want to make sure you can communicate well with students/parents, make everyone comfortable, make tutoring as "fun" as possible etc --not just a smart person with high scores. Your teaching experience and willingness to tutor all 3 sections will help.
The hours depend on demand. Summers or the late spring are busy because most kids take the test in May, June, Oct, Nov. You need flexible availability after school/weekends. Mine started slow and soon they were offering me more kids than I could take at a time (on top of my day job) but maybe they wanted to see what kind of results I got before giving me too many. If you do well I'd expect 4-15 hours per week during busy seasons but really depends on the company, location, your availability. Pay should be $25-$50/hr again depending on the company. My companies did not pay travel time but do expect you to be willing to drive 30 minutes to a house. Mine has been good about offering me some students right in a 10 minute radius. It's great money on the side but fluctuates so much I wouldn't recommend it as your main income.