Regarding compression hose, I need to wear them every day. I have edema in my ankles and legs, and the compression keeps the fluids moving throughout my system and dramatically improves my energy level. I have no idea if they will have such an energy effect for you for a single day's long flight, but they will surely prevent or at least reduce swelling.
If you go to a podiatrist or other doctor for a prescription, it will probably be for Jobst which is top of the line and e-x-p-e-n-s-I-v-e! They are also a bit of a pain to buy because you have to meet with a specialist to be measured and assessed. Without a pre-existing medical condition requiring them, they probably won't be covered by insurance. Over the years, I've bought whatever lower priced competing brand my local durable medical equipment store sells. These days, I'm wearing Sigvaris brand (mentioned elsewhere on these forums) which I'm very happy with because they're machine washable, dryer safe, and very durable. For your occasional use, only a day at a time, you probably won't care if the hose you buy need to be hand washed.