Does flexible schedule actually exist or is it BS?

My company just announced "flexible work arrangements" so I asked if I could do 7am-3pm instead of 9-5 so I could pick up my kids from school. My manager said "sure!" but now I'm getting emails at 3:15pm asking me to jump on meetings. Staying late defeats the whole purpose. Are any of you actually able to use "flexible" schedules without weird consequences, or is it just corporate theater?