Background: 2 years of working in Dubai
As far as I know, if you are working outside of the EU, you are regarded as non-resident and therefore not eligible for any reciprocal arrangements.
There is no state healthcare system for non-nationals in the UAE or KSA, it's an entirely private system.
Therefore you will need to ensure that any job you take provides health insurance that covers pre-existing conditions. Otherwise you could be looking at spending several hundred pounds a month on diabetes treatment.
Even when your insurance covers existing conditions, generally unless you are very lucky, it will cover the cost of insulin and your doctor visits and that's it. Test strips, pens, syringes, lancets, needles all tend not to be covered and will have to be paid for out of pocket. You can expect to pay around ?30 for a pack of test strips.
I've never tried to get needles in the UAE but insulins and test strips are freely available over the counter. However, without a prescription, you won't be able to get the cost back from your insurance, so you'll need to make a doctor's visit (which is chargeable to your insurance, typically you'll have to pay the first ?15 of the cost).
When I was there (2007-9), Novorapid, Lantus and Levemir were freely available so I would imagine Humalog is available too. Test strips are also easily available - don't forget that the Gulf has the second highest rate of diabetes in the world, something like a third of Saudis have T2. Care standards are a mixed bag depending on the hospital you use, and expect to find your insurance won't cover the best hospitals.
Finally, don't forget that the UAE and KSA have mandatory Ramadan, which is something else to consider. It's doable but can put extra stress on you.