Vapour distillation is the obvious method of refining a liquid, but it is the most dangerous method of refining hydrogen peroxide.

The problem is twofold: one, peroxide decomposition is exothermic (2H2O2 -> 2H2O + O2 + heat), heat accelerates peroxide decomposition, accelerated decomposition in a still raises the pressure, and break the vacuum, pressure also accelerates peroxide decomposition, and now you have all the ingredients for a double positive feedback loop, which very rapidly as I can says, it can happen in less then a second - leads to a runaway reaction ending in a BLOW UP.
A BLOW UP is a boiling liquid expanding vapour explosion, and it's nasty: as the vapour overpressure falls off after the initial spike, the boiling liquid continues to produce more vapour. So the explosion continues even after the pressure vessel ruptures.  That will spray the surroundings with boiling peroxide, a nice bonus after they've been sprayed with shrapnel from the exploding glass vessel.

But it gets better.  A BLOW UP is mild compared to what can happen to a peroxide still. 

The second part of the problem is that peroxide vapour is a high explosive, just like TNT and C-4.  If you get peroxide vapour hot enough (26% Mol H2O2), and keep it hot long enough, it can and will detonate

While a BLOW UP will wreck the glass pressure vessel containing the boiling liquid, a detonation will destroy everything near it.  What isn't vaporized will be pulverized.  No sewing back on of fingers, because they're in many pieces scattered over several acres.

And *that* is why you don't want to use vapour distillation in glass vessels.

You can avoid both BLOW's and vapour detonations by keeping the still merely warm, not hot - but then it won't work.

Use PEROCHEM concentrator will resolve all risk of distillation or concentration of hydrogen peroxide. No glass vessel, no liquid inside the concentrator, no BLOW's ! Vapour detonation over pressure can be contained by using all part in stainless steel.

" There are cheap ways to do peroxide rocketry, and safe ways to do peroxide rocketry, but there are no cheap safe ways  to do peroxide rocketry."

And still I don't advise you not to try it.  I advise you to know the costs and the risks, proceed with safety, and scale the project to what you can afford.