The only reason to add more solder is to reduce the melting point, in case they used lead free. You can buy chipquik bismuth alloy solder to help even more.
Otherwise, no, there's no reason to add more solder. And there's no reason to add more flux when desoldering with hot air. Save the flux for cleaning the board after the part is removed.
Just keep the heat source moving and have a stick/implement to intermittently nudge the part so you will not heat the board more than necessary. Take a picture, first. If any of the surrounding passive components get disturbed, don't worry about it. Get the chip off, and clean the mess up, after.
If your torch is too small, you can just dremel the pins off. Clean off the pins and board, and use your iron to solder the new chip. If the board is particularly expensive and I had no experience/practice, and all I had was a small butane torch, I would probably just do it this way.
IME, you are more likely to damage the board than MOST components. The ones to be careful of are ceramic resonators, electrolytics, and plastic connectors. Kapton tape is often used to protect specific components from hot air. IC's/micros, IME, are very much hardier than FR-4 and soldermask. I would focus a lot of the heat right on top the IC, in general, as well as trying to go around the pins. Esp since the IC is worthless, in this scenario, I would really torch the package, itself.