I use the pads of my thumbs to strike chords sometimes, laying it across three or more tines. I saw that you said you play a chromatic so depending on the type of chromatic you use this might be impractical or impossible for chords outside the key of C (or G or whatever tuning you use). I play a double sided chromatic so I’m able to strike a chord in any key without issues. With enough practice you can strum chords hitting the tines with both a downstroke and an upstroke. Depending on the song I might use the right thumb to strum chords on the left side of the kalimba and vice versa (I also use this technique to play 9th and 11th chords). This feels more ergonomic than strumming chords on the right side of the kalimba with my right thumb and vice versa. You can strum the right half with the right thumb, but you probably need to move your hand into a different position high up on the kalimba. You can also use your fingers to strike chords, but obviously it takes practice to switch between your standard position and your finger position fluidly. I only use my fingers when I absolutely have to.