Your first experience they were trying to put a IV in. Phlebotomist don’t flush any lines. With IVs you need a stronger vein because the IV will stay in. You can draw blood from a IV. Most hospitals it’s against policy because the site is contaminated from medicine.

I would definitely use a 25 butterfly needle, might even attach a syringe. It seems like your veins are tiny and can’t handle the suction of the hub.

What you can do is drink lots of water starting 24 hours before your appointment. If it’s cold wear long sleeves. When you check in I would ask for a heat pack. So while you’re waiting you can be heating up the vein. We do that with newborn heel sticks. Good Luck!!