Portable amp for Beyerdynamic T1?

I have the T1 version 3. 

It will be more business travel than personal, from here on the west coast to corp HQ in Boston, so a longer flight and often a stop (most of the nonstops are redeye, which I'm not doing).  There will be significant time both in the office there and in the airport/plane/hotel -- maybe I'll give your Bose suggestion a spin and see how it goes.  I've actually got a Bose wireless headset that they sent me for my home office, it may well be Quiet Comfort. 

My amp at home is not a small footprint -- ModWright LS-100, quite large for a preamp, actually. 

You will get hearing loss listening to non NC cans on a jet.

Don’t even consider it.

Airlines give out cheap ones. They don't care about your hearing.

With those headphones you can probably get by with an AudioQuest Dragonfly Red or Cobalt, but as they’re open-back ‘phones I don’t see them working on a plane at all.  You could buy reasonably-priced earbuds for the flight and use your T1s when not in the air, or you could buy the well-regarded Sony NC headphones that sound better and more accurate than Bose and you don’t have to let anyone know you bought Bose.  IMHO, Bose is better at cancelling sound than reproducing it.  FWIW…

https://www.amazon.com/Sony-WH-1000XM4-Canceling-Headphones-phone-call/dp/B0863TXGM3?th=1

I recommend taking a look at the Topping G5 if you can stretch your budget to $299. Slim case with good clean power output.

Note that the iPhone will require some sort of Lightning to USB adapter to connect to a portable DAC / amp.

I also agree with other posters that if you're going to try to listen to music on a plane, you really need active noise cancelling (ANC) headphones. I have a pair of AKG N400NC for travel. They sound great and ANC performance is decent. If you're interested in buying, I'd wait for Black Friday. They've gone on sale for as low as $39, I believe.

OP,

Definitely quiet comfort then. I live out side Portland Oregon and corporate headquarters was in New York for me for nearly 20 years… although most of the time I flew globally. You want wireless Bose. As a company I have hated Bose for masquerading around as high end. But they got Quiet Comfort right (not high quality but perfect for travel in noisy environments). Look into business class… half the folks are wearing them. 
 

I know a seasoned business travelers when I see khaki cloths, a Nikon or Arcteryx hat and Bose Quiet Comfort headphones in the Delta Lounge. We are the road warriors, seasoned and optimized to make flying as comfortable and enjoyable as possible.