Let’s start with the legend of ten thousand ships, which is probably an exagerrated way of saying “a lot of ships” in the same way that a lot of numbers reported for ancient and medieval battles are. If a small warship can hold 100 people, that suggests a mass migration of a million people. That’s your high-end figure.
However, Nymeria’s journey was pretty rough – attacked by corsairs in the Basilisk Isles, a failed resettlement in Sothoryos, plague in Naath, a split in the Summer Isles, etc. etc. – which is going to bring one’s numbers down. So even if we start from the high-end figure, I would guess that about a half-million made it to Dorne.
What we do know is that Nymeria’s survivors increased the strength of House Martell tenfold (although again, that could be an exagerration) and gave them enough strength to overcome the Yronwoods and the other Kings of Dorne.