A lot of people have said that Florida seems to be particularly backward regarding oxygen.
It sounds to me like maybe they're intending to give you a concentrator (a machine that makes O2 from room air), not cylinders. No good, concentrators. This is what they're used to providing (for old folks with COPD) -- a concentrator with a limited built-in regulator, and nasal cannula (and maybe a tiny portable cylinder that would be practically useless for you)
I've sent you a PM about a small part of this. But you have to persist: You want at least one large tank (an "M" tank or an even larger "H" tank) and at least one smaller, portable tank (an "E" tank), both with the regulator your doctor prescribed, and an non-rebreather mask (which the doctor should also have prescribed). Usually the prescription specifies the lpm and the non-rebreather mask ("NRB mask"), but not how much O2 is provided and in what form. A good provider will give you multiple large tanks and multiple smaller tanks.
jon019 is right that once you get the proper tanks and mask, you can buy your own regulator for higher flow rates. But I would think that it is legally required for them to provide the flow rate that your doctor specifies. Before you buy a regulator, you have to know what size tanks you have. For medical oxygen, the larger tanks take a different type of regulator (CGA 540) than smaller tanks (CGA 870). If you get a 15 lpm regulator, or even a 12 lpm, it just might be good enough for you.
I have found that oxygen suppliers are willing to be educated about CH. Many of them have never supplied O2 to someone with CH. Often they have a respiratory therapist on staff who might be willing to talk to you. This is a link to the JAMA article, which might be something you want to provide to someone at one of your possible suppliers. http://jamanetwork.com/journals/jama/fullarticle/185035