It is from the term "Philistines" that the name "Palestinians" has been taken. Actually, the ancient Philistines and modern Palestinians have something in common: both are invaders from other lands! That is precisely the meaning of their name, that is not an ethnic denomination but an adjective applied to them: Peleshet, from the verb "pelesh", "dividers", "penetrators" or "invaders". The Philistines were a confederation of non-Semitic peoples coming from Crete, the Aegean Islands and Asia Minor, also known as "Sea Peoples". The main tribes were Tzekelesh, Shardana, Akhaiusha, Danauna, Tzakara, Masa or Meshwesh, Lukki, Dardana, Tursha, Keshesh or Karkisha, Labu and Irven. The original homeland of the group that ruled the Philistine federation, namely the "Pelesati", was the island of Crete. When the Minoic civilization collapsed, also the Minoic culture disappeared from Crete, as invaders from Greece took control of the island. These ancient Cretans arrived in Southern Canaan and were known as "Pelestim and Keretim" by Hebrews and Canaanites (that became allied to fight the invaders). Their first settlement seem to have been Gaza, whose original name was "Minoah", a clear reference to the fallen Minoic kingdom. They also invaded Egypt and were defeated by Pharaoh Ramose III in the 12th century b.c.e. The Philistines were organized in city-states, being the most important the Pentapolis: Gaza, Ashdod, Ashkelon, Gath and Ekron, and their territory was close to the Mediterranean coast, a little longer and broader than the present-day "Gaza Strip" - not the whole Judah, they never reached Hevron, Jerusalem or Yericho!
Those Sea Peoples that invaded Egypt were expelled towards other Mediterranean lands and did not evolve into any Arab people, but disappeared as distinguishable groups in Roman times.
Those dwelling in Canaan were defeated by King David and reduced to insignificance, the best warriors among them were chosen as David's bodyguard. The remaining Philistines still dwelling in Gaza were subdued by Sargon II of Assyria and after that time, they disappeared definitively from history. They are no longer mentioned since the return of the Jewish exiles from Babylon.
Conclusion: there is not one single person in the world who may be able to prove Philistine lineage, yet, if Palestinians insist, they have to recognize themselves as invaders in Israel, and then they must ask Greece to return them back the Isle of Crete! The Philistines are extinct and claims to alleged links with them are utterly false as they are historically impossible to establish.
In any case, claiming a Philistine heritage is idle because it cannot legitimate any land in which they were foreign occupants and not native dwellers. Philistines were not Arabs, and the only feature in common between both peoples is that in Israel they should be regarded as invaders, Philistines from the sea and Arabs from the wilderness. They do not want Jerusalem because it is their city, which is not and never has been, they simply want to take her from the Jews, to whom she has belonged for three thousand years. The Philistines wanted to take from Israelites the Holy Ark of the Covenant, modern so-called Palestinians want to take from them the Holy City of the Covenant.
The Palestinians: No, they are not any ancient people, but claim to be. They were born in a single day, after a war that lasted six days in 1967 c.e. If they were true Canaanites, they would speak Hebrew and demand from Syria to give them back their occupied homeland in Lebanon, but they are not. If they were Philistines, they would claim back the Isle of Crete from Greece and would recognize that they have nothing to do with the Land of Israel, and would ask excuses to Israel for having stolen the Ark of the Covenant.