Unless you hot-desk (and even then, with a bit more effort) it should be possible to take your own mug to the office and use that to microwave instead of a styrofoam cup. Note that it's worth being a bit cautious when adding anything to water microwaved to boiling point - I would use a spoon to insert the tea without putting your hand or face above the mug.
That recipe actually says there are two ways you can prepare this:
There are two ways to do this: throw just about everything in a pot of
water and simmer, then add the milk, tea and sweetener and brew for a
few minutes; or, let the spices soak overnight in the water then
simmer in the morning with your tea leaves and milk.
(emphasis mine)
Have you tried the latter? That way you still only have to heat things up once.
I'd be hesitant to boil milk with spices and then store it cold, reheating again. If you're using dairy milk, that is. If you're using anything other than non-fat (skim) milk, you'll get a "skin" on the top of the milk when you're boiling it - that's one of the classic signs of masala chai for me. But anyway, it becomes substantially less appetizing if it has time to cool into globules and is then reheated again. I'm not sure what problems, if any, you'd encounter using non-dairy milk like almond or soy.
You could dump the pre-ground spices into your brewed tea with milk and sugar, but the flavor profile will be a little different. Boiling the spices with the milk and tea gives everything time to meld nicely and provide a really smooth flavor blend. But I don't see any especially compelling reason that you couldn't do it.
I would like to point out, though, that boiling enough water for a travel mug's worth of tea doesn't take any more time to do on the stove than it does in my electric kettle. Adding milk shouldn't make too much difference; I'm willing to bet that after you get familiar with the routine, you can follow this recipe and still have it take 5-6 minutes. :)
Purists will insist that the spices must be boiled with the water, but those are the same people who would scoff at you adding cold milk to your tea in the first place. There's no reason why you can't, other than it might cool down the rest of your tea.
Best Answer
Why not make it how you like it at home? Here's your best bet (and a very simple suggestion); buy a good thermos. You can get a 24 ounce one for about $30 which will work incredibly well, and last you a lifetime unlike most cooking appliances. When you properly prime a thermos with boiling water, it can keep beverages piping hot for upwards of 12 hours. This lets you avoid trying to come up with a complicated solution at work.
Boil water and put it in the thermos, and seal it. Leave it alone for a few minutes while you brew your tea exactly as you want it. When your tea is ready, dump out the boiling water and pour in the tea, and reseal.
We do this daily for my wife, since she is unable to brew tea at work. She just uses hot water, but it stays hot enough that she can actually drop in a teabag or two midway through the day and brew with no issues. Here is the one we use: http://www.amazon.com/gp/product/B008FK9NIC