How can I have two alerts on one view in SwiftUI?

The second call to .alert(isPresented) is overriding the first. What you really want is one Binding<Bool> to denote whether the alert is presented, and some setting for which alert should be returned from the closure following .alert(isPresented). You could use a Bool for this, but I went ahead and did it with an enum, as that scales to more than two alerts.

enum ActiveAlert {
    case first, second
}

struct ToggleView: View {
    @State private var showAlert = false
    @State private var activeAlert: ActiveAlert = .first

    var body: some View {

        Button(action: {
            if Bool.random() {
                self.activeAlert = .first
            } else {
                self.activeAlert = .second
            }
            self.showAlert = true
        }) {
            Text("Show random alert")
        }
        .alert(isPresented: $showAlert) {
            switch activeAlert {
            case .first:
                return Alert(title: Text("First Alert"), message: Text("This is the first alert"))
            case .second:
                return Alert(title: Text("Second Alert"), message: Text("This is the second alert"))
            }
        }
    }
}