You almost can run those little drills too fast to burn them up, even HSS.
They want a surface speed of up to 200 SFM, which is far from burn up territory.
A #80 (0.0135") bit needs to be spun at 56,000 rpm to hit 200 SFM if you run the numbers through G-Wizard. Applications that drill a lot of tiny holes all use very high speeds to do it. Dumore and others made small "sensitive" drill presses that ran at 20-30K rpm for the purpose.
You can absolutely drill holes with a lot less speed than that, just trying to point out what the feeds and speeds look like.
When you burn a tool, it's too much SFM. When you break a tool, it's too much chipload. That same #80 bit wants a chipload of 0.0005". You can feed a right smart 56 IPM to get that chipload at 56K rpm. However, let's return to reality here (unless you have an aux. Dremel or Proxxon spindle on your mill, which would be handy for this!), and try it at 2000 rpm. Now your maximum feedrate is 2 inches per minute. Let's take half that feed in our home shops to get a little more life. 1 inch per minute. That's 1mm per 2 seconds roughly.
Feed these bits REAAAAAALLLLLLLLLLLL SLLLLOOOOOOOOOOOOOOOOOWWWWWWWWWWW! And a sensitive finger touch chuck, pecking, blowing away the chips, a little lubricant, and a prayer or two wouldn't hurt either.
Cheers,
BW