I'm T2 and also have attacks of gout.
I was diagnosed with T2 in spring 2015, after almost 10 years in the pre-diabetic range. I take no medication, because so far, my highest HbA1c has been 48 (lowest 46). I went on an X-PERT course last year, learnt about carb counting and over the last 18 months made steady changes to my diet, decreasing the amount of carbs and increasing the proportion of protein foods, including more animal protein than I'd had for decades. For a big chunk of my life I was vegetarian or vegan, and I'd never gone back to eating much animal protein and I've always had a higher-than-average percentage of fresh vegetables and fruit in my diet.
Then 3 months ago I had my first attack of gout, and have now had 4 - despite medication and changes in my diet, cutting out all the high purine foods. So my diet is now much closer to what it was before the advice to change to a low-carb diet, and my HbA1c has gone from 47 to 48 (because as they keep blood testing me for the gout, they also repeat the HbA1c tests). My doctors are telling me not to worry at all about that amount increase in the context of the whole situation, and talking through the details of the diet changes I'd made, they all seem to agree it could be what's taken my uric acid levels up to the levels that have caused the gout.
For the broader picture, I have gout in the family, my BMI is 34, I've had an injury to the toe joint which was the first to have symptoms, and I've had a period of long-term stress. And I'm T2. All of those are relevant. There's a lot more to the whole picture than red meats and high sugars (fructose in particular).
I'd recommend the UK Gout Society website - there are good factsheets you can download.
http://www.ukgoutsociety.org/ The NHS website's good for a basic level of information, but might not tell you enough (I think).
http://www.nhs.uk/Conditions/Gout/Pages/Introduction.aspx If you want more in-depth information, the NICE Guidelines are good - you'll see why your doctors are giving you the treatment you're getting.
https://cks.nice.org.uk/gout
Just beware any website linked to selling you anything!