Based on everything you've endured, his abusive nature, the tone of that message, your knowledge of his family history and so on, my gut feeling, like so many others have already suggested, is that he's lying... and this latest contact is designed to distress you and/or effectively force you to engage with him.
I absolutely understand how worried you must be. My oldest child's paternal grandmother was diagnosed with HD when I was 7 months pregnant. This was 30 years ago before the specific genetic test had been developed so we had no way of finding any further information about my child or their father until 5 or 6 years later. Thankfully their father wasn't a carrier, although his 3 siblings all are.
In this case, my ex's mother had displayed a variety of symptoms for around 15 years before diagnosis but no one had put 2 and 2 together for a long time not least because she had had a fractured family history so the indicators present in other relatives went largely unnoticed as there was very sparse contact. It's therefore unlikely (though obviously not impossible) that if your ex had a relatively normal upbringing, that something would have been known within his family about HD. It beggars belief, for example, that if his father's sister had it, that his father would not have been aware of the potential implications for himself given that either his/their mother or father would also have had to carry the gene. This is the sort of thing which would become absolute accepted knowledge within the family because it's so significant, e even if individuals chose not to pursue genetic testing. In short, I find it hard to believe that you would have been unaware of this until now... and dare I say it, I suspect, due to his narcissistic and abusive nature, that he would have 'milked' even the possibility of him carrying the HD gene for sympathy long before any actual confirmation that he does. Again, it's not impossible due to the vagaries of human nature that he kept this quiet previously but on the balance of probability, it's far less likely.
All that aside, the point is, in your case, that you need to establish the truth of his allegations via safe and appropriate channels before panicking. I appreciate that's easier said than done now he's planted this seed but please try not to stress too much until you have concrete facts in front of you. Some of the advice given in this thread, albeit well meaning, about the manifestation of HD symptoms and testing etc is actually wrong and I'm concerned that it may add to your understandable concern. The best possible advice and information will of course come from specialists if and when (and hopefully this won't be the case anyway) you have genuine cause to investigate further. In the meantime, because I know it's difficult not to search for answers/reassurance when hit by something like this, the Huntington Disease Association site is a very reliable and informative resource.
I wish you luck and hope this is sorted out asap. Regardless of what happens you do not need to engage with him. He really is a vile shit by the sounds of it and I hope, in the circumstances, this is 'just' another of his sick schemes.