J-35 will likely carry anything flanker would lift; other than Su-34, flankers aren't exactly known for extreme single weights, and even much smaller aircraft can normally take heavier payloads. The problem isn't so much taking, it's likely higher negative impact to Cd(already imacted by bulkier airframe), less internal fuel, and lesser number of external stations.
True (brahmos notwithstanding but thats irrelevant anyways), the reference to yj15 was more along the lines of "its small enough that even the smaller-than-flanker J35 would be comfortable carrying and using".
wrt the negative impact to Cd, internal fuel and number of external stations I don't think there's a lot to worry about.
Cd: True in a vacuum, but we have to consider a few nuances.
1: The J35 is designed around nearly 40 years after the Flanker and the computational capacity has increased tremendously, allowing designers to make aerodynamic gains by more thoroughly optimizing the airframe. I would suspect that this alone offsets the Cd penalty to some extent.
2: We also have to consider that modern fighters usually carry a few A2A missiles even in strike missions, and J35 carries these internally with no additional compromises to its aerodynamic shape. Overall I do not expect the drag coefficient increase to be overly worrying.
Internal fuel: According to yankeesama the Air Force J35A has at least 7t internal fuel (source is one of the podcasts either this or last year, I'll have to look it up). If we assume the naval J35 has similar capacity then it should be plenty enough for any operations within reason. Remember that fuel quantity is not the only determining factor of range, you also need to consider aircraft weight (J35 would be lighter), as well as tsfc, and L/D, both of which I would assume J35 (having a newer engine design and having undergone better aerodynamic optimization) is at least comparable to the J15T.
External stations: Its safe to assume J35 has at least 4 wing hardpoints that have decent weight limits. imo 4 is more than adequate for any strike missions, seeing as even Chinese flankers seldom carry more than 4 anti ship missiles a la yj83 (yj91 yes, but thats lighter and smaller iirc).