Picking two different images in the same view controller using imagePickerController in Swift

You only need one UIImagePickerController. You can keep a reference of the tapped view and when the user finish picking the image, you just need to cast the selected view as UIImageView and set its image property:

update: Xcode 11.5 • Swift 5.2 or later

import UIKit

class ViewController: UIViewController, UIImagePickerControllerDelegate ,UINavigationControllerDelegate {
    
    @IBOutlet weak var imageView1: UIImageView!
    @IBOutlet weak var imageView2: UIImageView!

    var imagePicker = UIImagePickerController()
    var selectedVew: UIView!
 
    override func viewDidLoad() {
        super.viewDidLoad()
        
        imagePicker.delegate = self
        imagePicker.sourceType = .savedPhotosAlbum
        imagePicker.allowsEditing = false
        
        [imageView1,imageView2].forEach {
            $0?.isUserInteractionEnabled = true
            $0?.addGestureRecognizer(UITapGestureRecognizer(target: self, action: #selector(chooseImage)))
        }
    }
    
    @objc func chooseImage(_ gesture: UITapGestureRecognizer) {
        if UIImagePickerController.isSourceTypeAvailable(.savedPhotosAlbum) {
            selectedVew = gesture.view
            present(imagePicker, animated: true)
        }
    }
    func imagePickerController(_ picker: UIImagePickerController, didFinishPickingMediaWithInfo info: [UIImagePickerController.InfoKey : Any]) {
        (selectedVew as? UIImageView)?.image = info[.originalImage] as? UIImage
        dismiss(animated: true)
    }
    
    func imagePickerControllerDidCancel(_ picker: UIImagePickerController) {
        dismiss(animated: true)
    }
}