No
Bastards have no right to inherit property. However if a bastard gets legitimizedlegitimised as the son of the lord, they can infact inherit the property. An example of this is Ramsay Bolton, formerly known as Ramsay Snow, who was legitimizedlegitimised by his fatherKing Tommen Baratheon on behest of Roose Bolton and became Ramsay Bolton, the rightful heir of his father.
Robert
Robert Baratheon however never acknowledged Gendry and did not legitimizelegitimise him, therefore Gendry had no right to claim Storm's End.