As some who recently started PD, I looked for information about flying/traveling while on PD and found this thread. I am wrapping up a week long trip so I figured I'd add what I found.
I took my cycler with me, I have the Baxter Amia which I ended up buying an 18" upright rolling bag to carry. My clinic lent me a case but it is a case designed for the older cycler (HomeChoice Pro) and I was concerned that it would not fit in the overhead. I have a letter from Baxter to give to TSA describing what the machine is. The letter also clearly states that the cycler has a lithium battery so per FAA regs, it should not be checked.
Baxter will drop ship solution to our hotel which some advance notice. Generally you need to provide them with your hotel reservation's confirmation number and then either they will ship or have a driver drop off boxes of solution. Note that you need to bring supplies with you (drain bags, cassettes, minicaps, etc). This is mainly because the supplies are shipped in quantities of 30 so unless you are traveling for a month, they're not going to drop ship you 30x of supplies for a week.
I opted to ship most of the supplies ahead of time. I shipped it FedEx Ground. As FedEx may get delayed or missing shipments, I did pack a couple of cassettes and all my minicaps in my carry on. I also put a couple bags of solution into my checked luggage. It's unclear to me whether or not TSA would allow you to carry on bags of solution. They are medical supplies but given that the agents who screened were unsure about my cycler, I'm not confident that an unknowing agent wouldn't throw out the solution.
Prior to travel, I called Delta's Disability Desk to inform them I'd be carrying my cycler. As a result, my reservation was flagged medical request and I was unable to check in online or at the kiosk. I had to check in with an agent which given the reduced number of check in agents means that you need to factor in additional time to wait. Frustratingly, there was nothing special about my check in once I got there. Makes me think that in future, I won't be calling them.
Additionally, you should plan for additional time to go through security. I have TSA PreCheck so I didn't have to remove my shoes or go through the microwave machine. However, my cycler was subject to secondary screening and I was patted down as a result. I've been told that the betadine that are used in the minicaps can leave residue on the cycler which when swabbed for explosives could yield a false positive. The TSA agent was very respectful and I informed him that I had a catheter in my abdominal area during the pat down. Not the end of the world, but just bear in mind that you need to allot more time for screening.
That's probably the biggest adjustment to traveling with PD, you can't travel light anymore and you certainly can't go from curb to gate in 10 minutes.