Answer: The most accepted guess is: By bamboo rafts.
Explanation:
There are two hypotheses.
The first is that they arrived on Flores as Homo erectus and then evolved to Homo floresiensis. The second is that they were already Homo floresiensis when they arrived. This second one is the more accepted hypothesis because it would take organization and language to accomplish this technological water transportation feat. Homo erectus is not known to have developed speech.
Now at the time this transport was estimated to have happened, 100000 years ago, the islands of Komodo and Flores were joined and visible from the mainland. Together they constituted a 19km wide straight visible that could be easily seen from the mainland. The Homo floresiensis tribes built bamboo rafts, or possibly some other floating apparatus made if wood, and sailed there. The islands then progressively drifted apart, isolating them.
PS: It is important to note that some things may have drove them there such as famine, violence, etc.
