If you’re having a conversation with someone and they keep pressing their phone then you stop talking! It is that simple. If you don’t want to stop talking, it must mean that what you are saying is more important, and right then, than whatever the person is dealing with, which, often, they don’t know until they look. Sometimes those messages can be very, very important! If they care about what you are saying, they will check and make a decision of what to deal with. But this answer is about you, not them. Let people make their choices, otherwise you are left coercing them into listening to you, which, put plainly, is not inspiring for them nor for you. So, make a point of thinking about and remembering where you were in what you were saying, so you can go back to it. This is for an actual interruption, where the conversation might be shortly continued. When someone looks at their phone, they are not saying “I’m not interested.” It simply doesn’t mean that. You can actually ask if they are interested, but be aware that many people, out of politeness, might not straight-out tell you, “No,” even if they don’t have the slightest interest. However, you can make it easy with indirect questions that allow them an easy escape without being rude, and, incidentally, without setting yourself up to feel bad.
“You seem distracted. Is this a good time to talk about this? How much time to we have to talk? Do you need to get somewhere? I’d rather talk at a time when you will be fully available. Is there something you’d like to talk about? Is something on your mind?” Now, someone who is always doing something else, which can be disconcerting if you are talking, you can directly ask for full attention, always without blame. If they want to do something else, that’s okay. However, you may not want to talk with them if they are doing that, so you give them a choice. What does not work is blaming them for being distracted. Simply stand for what you want without forcing them to do anything. They can listen or not, and you will speak or not, depending on their choice. You could call them rude, but you could also realize that you failed to engage them, if you want to go into blame and fault. I don’t recommend it. Just be authentic, be straight with people. Let them be who they are, and you will find, often, that people are spectacular, just not necessarily in ways that you expect.