I have had the same issue when machining aluminum parts with small end mills. Getting feeds and speeds correct for your particular alloy can usually prevent gumming up cutting tool.
I imagine you are probably cutting freehand so consistent feed is pretty much impossible, and you may not be using a tool that is easily speed adjustable, probably an air grinder? So regulating speed might not be easy either.
As far as lubricants, might not work for your application being a liquid, but I use WD-40. It produces a nice clean cut, and flushes chips out of the way and keeps them from sticking to the cutter and gumming it up.
(I don't know if you guys have WD-40 in your country, maybe someone knows of an equivalent light 'penetrating' oil/solvent.)
I know that carbide burrs for aluminum do exist, they will have a different number and shape of cutting flutes.
You may be able to find Zirconium Nitride coated carbide burrs. Those would definitely help prevent build up, but they won't be cheap. The coatings do eventually wear off, and you are left with a regular carbide burr.
If you don't fancy using an oil or wax based lubricant, like if you are planning on welding were you are grinding, I have heard of guys using diluted dish soap to machine aluminum. I have never tried it personally. I imagine just the water keeping the cutting tool cool would help with the build up some, and the soap might do the rest.
Maybe somebody that welds aluminum by trade will chime in. I'm assuming if they weld it, at some point they have to grind it too.
Some alloys are just more 'sticky' than others. There may not be a good/easy/cheap fix. Might just have to stop and clean them out every now and again. Really depends on how quick they pack up and how much you have to grind.
What's the project, if you don't mind my asking? Maybe the real solution is to just go about it in a completely different way?
Sorry, I just realized I wrote a book there, but didn't actually help very much.