Yes, you can cross stitch on a flight and all your tools can be taken in your carry-on bag. The TSA advises;

You may place your knitting needles and needlepoint tools in carry-on or checked baggage.

However, it should be noted that you are only allowed to take scissors as long as the blades do not exceed four inches.
 
Let’s go a little further into this and work out exactly what you might need in order to take your cross stitch with you when you travel.
There are two things to think about here, the needles and the scissors. You can take both on a flight, so long as you prepare for it.

 

Can You Take Cross Stitch Needles On Planes?

Yes, you can take cross stitch needles on a flight.
 
The TSA advises all needles should be enclosed in a hard shell when not in use.
The best approach here is to buy something like John James Pebble, as it’s clear, so the TSA agents can see, they’re enclosed, and they stay they’re embroidery needles (this is rarely asked, but helps to show it). Limit the amount you bring though, you’re not taking an arsenal and they might look at you weirdly if you have 100 needles with you.

I will add a caveat there, that sometimes needles can be confiscated if there is a heightened risk. If this is the case, all airports carry sewing kits, which can be picked up for $2-3, and contain a needle (oh, the irony). In some cases, these are even embroidery needles. Just be careful with the point.

Can You Take Cross Stitch Scissors On Planes?

Yes, you can take scissors on your flight.
The TSA advises;

Scissors must be less than 4 inches from the pivot point. Any sharp objects in checked bags should be sheathed or securely wrapped to prevent injury to baggage handlers and inspectors.

 
What you’re ideally looking for is a pair of scissors that are less than 1 inch from the pivot point, and are rounded off on a 1/1 curve and aren’t larger than 4 inches total. However, I was not able to find a pair like this in my research, but they don’t strike me as very useful tools for cross stitch.
There are safe alternatives though. In fact, these alternatives are not only safe to travel with, but are easier to use too.

Micro Scissors

We’ve actually written up a whole post on micro scissors for cross stitch, and why you might want to use these when you’re not traveling as well (they are super easy to use), but they are perfect for travel as the whole thing is about 2 inches. They’re specifically made for needlecraft, and cheap to pick up too.

Thread Cutters

Whilst we used to suggest takign thread cutters; some TSA agents in the US (and at the moment only the US) have advised that you can’t take these either! So keep to those less than 4 inch scissors!

Circular thread cutters or any other cutter or needlepoint tools that contain blades must be placed in checked baggage.

Now you have everything prepared, place both needles and scissors (if you have them) in a clear bag, and treat them like liquids.
 
On a final note, I would suggest in all cases you should phone the airline before taking them aboard, and NEVER hide them. Also, as a tip, use shorter lengths of thread than usual, you don’t have as much space on a plane.