Bonide Poison Ivy and Oak Killer RTU is safe as long as you follow all proper instructions per product label. Pets and children should not be around during application and it is safe to come back once everything has dried.
With English ivy, because it of the waxy leaves, we do recommend a brush killer. It is possible that it could kill the perennials if you are not spraying carefully. You will need to do a spot treatment with Bonide Poison Ivy and Brush Killer. Also, this product is for use on Bluegrass, Fesue, Rye, Bent, Bermuda, Bahia and Zoysia Lawns. Avoid application to St. Augustine or centipede lawns unless injury can be tolerated. Do not spray Carpet grass, Dichondra or desirable clovers. May cause temporary yellowing of some Bermudagrass turf. Do not exceed specified dosages for any area. Be particularly careful applying within the drip line of trees and other ornamental species. Avoid contact with exposed feeder roots of ornamentals and trees.
Unfortunately, post-emergent herbicides that will kill the poison ivy effectively would likely also damage the flowers. It would probably be best to cut as much of the ivy as possible and then yes, spot treat with a vine killer such as Bonide Poison Ivy and Oak Killer RTU or Bonide Poison Ivy Brush Killer BK32 Concentrate.