First, you wont' need any amps of battery to do a specific distance. You would need a certain number of amp-hours, however. It is a VERY important difference; if you mix them up when buying a battery you're not going to get what you need.
Second, I wouldn't assume completley flat with no headwind for your calculations--nothing is ever really flat, and there's never really no winds at all, almost certainly not for a trip that long. I don't think you'll want to have to camp out on the roadside waiting for every breeze to stop just so you can make it to the destination, and you absolutely don't want to run out of power before you get there.
But if you like you can assume that, and probably take around 25wh/mile for 20MPH (which means a miniumum of 11 nonstop hours of riding for that 220mile leg). So if you used 25wh/mile for 220 miles, that would be a minimum of a 5.5kwh battery. That's very large and heavy. My 2kwh hour EIG pack on the trike is about 35lbs, and the size of a stack of hardback books. Your battery will have to be almost three times that size, minimum, so call it a little under a hundred pounds of battery, the size of a small human torso.
I'm guessing that the 220 miles is not a door-to-door distance, but just the basic distance between cities. If so, then you should add at least several dozen miles to account for in-city routes and detours, between recharges, so you don't end up stuck somewhere. So you could just go with a 6kwh battery, minimum.
Keep in mind you can't necessarily go by the advertised battery specs, either--many of them cannot deliver the "rated" capacity because they've calculated that based on the individual cells' lab-tested specs that go from completely full to completley dead, and if the pack has a BMS it won't let you drain them that dead (it shouldn't, anyway). Then you have to allow for the cell quality (or lack thereof) in most battery packs, that wont' actually let you get the full capacity because of cell variation, imbalance, etc.
So you may have to add 20-25% to the expected capacity, to guarantee you will not run out of power somewhere between cities. That brings your pack up to about 7.5kwh, so it's now well over a hundred pounds and the size of a largish human torso. Not sure where you're going to carry that on the scooter, unless you've installed panniers or are going to pull a trailer.
Then, if you want to allow for wind and hills, and potential detours, you may have to add another 20-25%. The pack is just getting bigger and bigger and heavier and heavier. At this point it's added so much to the scooter that it's going to take some of the battery power just to move itself, and you may have to start making teh pack bigger to account for that.
If you need to go faster than 20MPH, the pack grows even larger even faster, because power usage due to air resistance goes up rapidly after that point.
I'm pretty sure you'll be better off pulling a trailer with a small *reliable* gasoline generator capable of putting out at least as much power as you'll need to keep the battery charged (or stopping for long enough to let it recharge the pack whenever it gets low), and using just a small battery that takes care of your in-city usage needs. It'll cost a lot less, be smaller, and weigh less, and you can sell it once you're at the destination if you're not going back..