We know that Elijah was persecuted from his own words:
1 Kings 19:14
And Elijah said, I have been very jealous for the LORD God of hosts: because the children of Israel have forsaken thy covenant, thrown down thine altars, and slain thy prophets with the sword; and I, even I only, am left; and they seek my life, to take it away.
We have from the Book of Jeremiah (38:6):
Then took they Jeremiah, and cast him into the dungeon of Malchiah the son of Hammelech, that was in the court of the prison: and they let down Jeremiah with cords. And in the dungeon there was no water, but mire: so Jeremiah sunk in the mire.
Stephen may also have been alluding to this passage in Chronicles:
2 Chronicles 36:15-16
And the LORD God of their fathers sent to them by his messengers, rising up betimes, and sending; because he had compassion on his people, and on his dwelling place: But they mocked the messengers of God, and despised his words, and misused his prophets, until the wrath of the LORD arose against his people, till there was no remedy.
Further, the books of the Prophets do not document their entire lives. Much of what was known about how the Prophets lived out their lives came from extra-Biblical Jewish tradition - oral or written. Most of this tradition has found its way into the Synaxaria (Lives of the Saints) in the Eastern Orthodox Church. In the non-Chalcedonian tradition, there is a reference called the Book of the Bee, which includes a chapter entitled "On the Death of the Prophets; How they Died, and Where Each One of Them Was Buried". The Eastern Orthodox Synaxaria include the accounts:
The Prophet Isaiah died a martyr’s death. By order of the Jewish king Manasseh he was sawn through by a wood-saw. The prophet was buried not far from the Pool of Siloam.
Ezekiel was condemned to execution because he denounced a certain Hebrew prince for idolatry. Bound to wild horses, he was torn to pieces. Pious Hebrews gathered up the torn body of the prophet and buried it upon Maur Field, in the tomb of Sim and Arthaxad, forefathers of Abraham, not far from Baghdad.
The idolatrous priest Amaziah of the pagan temple particularly hated the prophet. The prophet predicted speedy destruction for him and all his household, and for this he was subjected to beatings. Hosiah, the son of Amaziah, struck the saint on the head with a club and seriously wounded him. Still alive, the Prophet Amos reached his native village and died there around 787 B.C.
I assume that the above or similar accounts can also be found in the rabbinic tradition (e.g. Talmud), but I haven't confirmed.
Stephen was certainly speaking hyperbolically - not all of the Prophets were martyred - but his statement in Acts seems to reflect a more or less common knowledge of those martyric deaths that did occur.