Portable amp for Beyerdynamic T1?

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. 

Thanks to everyone for their comments.

Turns out I've got both my own personal pair of sony NC phones (MDR-ZX750BN) and my company-supplied Bose QC phones.  I'll take both on my next trip and see which works better on the plane.  I've used the Sony on the plane in the past, and they were good at canceling noise and gave decent sound quality, but I was aiming to improve my sound quality if I could.

@yage -- I can stretch to $300, will read some reviews on the G5 to see if it works for my use cases. 

I ended up buying a Topping G5, thanks, @yage.  Looked like just what I wanted.

@lee_short You're welcome - hope you enjoy!