Is there any penalty to using a lot of chained promises together

What you're doing there seems really nice and clean.

The downside is that when it first starts, it's using a bit of memory to store all the promises all at once, but it's not really that bad.

If you nested everything with callbacks you'd avoid that up-front memory usage, but then it ends up re-parsing all the functions inside each time it goes through an iteration, so there are downsides there too (in addition to it looking awful).

Only other thing I might mention is if you're just doing:

spiWriteCommand(X);
return hspi_cmd(Y);

over and over, you could create an array, like:

var data = [
 [[sizeH-1,0,0],0x0C],
 [[0xD7,0xD6,0x9D],0x2C],
 [0xA8,0x3A],
 ...
];

promise = new Promise(resolve => {
  function out() {
    var cmd = data.shift();
    if (!cmd) return resolve();
    spiWriteCommand(cmd[0]);
    hspi_cmd(cmd[1]).then(out);
  }
  out();
});

but I wonder if that's really better - i'd stick with what you have for now