The people you'd never think to say it to
So far this has been about the people you're close to. There's a whole second drawer for everyone else. The woman on the platform in the coat. The man at the deli counter who's cheerful at eight in the morning. The bus driver who waited. Your neighbour's front garden. The stranger's dog. With these people you don't even get as far as the squirm, because it would never cross your mind to say anything. Compliments are for people you know.
I'd question that on two grounds. The first is that the stranger is the easiest case there is. There's no history, no fourteen years of silence to break, nothing at stake and no ask you could possibly be softening them up for. You'll never see them again. Every reason the drawer gives for keeping the thought in is weaker with a stranger than with anyone else, and the compliment studies included plenty of people who barely knew each other, with the same result. Recipients felt better than the givers guessed.
The second is what these small exchanges do for the person having them. Gillian Sandstrom and Elizabeth Dunn published three studies in 2014 on what they called weak ties, the acquaintances and near-strangers on the edge of a person's life. Students were happier and felt more belonging on days when they'd interacted with more classmates than usual, and in two further studies covering all of a day's interactions, contact with weak ties went along with wellbeing in the same way as contact with close ones. That's about interaction generally, not compliments, and it doesn't show which way the cause runs. But it suggests that the platform and the deli counter aren't nothing. They're part of the day's social weather, and a good thought said out loud there changes it a little for both of you.
Here's the practical part, which is mine. The stranger's compliment has to be about a thing, not the person. The coat, not the figure in it. The garden, not the gardener. The dog. Keep it to what they chose or made, and keep it short, and keep walking if that's what you were doing. "That's a great coat" as you pass is complete. It needs no reply and usually gets a surprised one.
I'd use strangers as practice, honestly. If the kitchen is too big a first step, the deli counter is a small one, and the landing is easy to watch. Say one to someone you'll never see again and see what their face does. That's a data point for the guess, the kind chapter 13 said you've been missing, and it costs you a sentence on a platform.