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I am trying to find the velocity of an object during re-entry so that I can calculate the peak heat flux but I'm a bit stuck.

I know how to find the velocity of the original, circular orbit (300km) but I don't know how to calculate the velocity while moving through the atmosphere.

The object is a small sphere, decaying naturally due to atmospheric drag, on a purely ballistic trajectory with no lift or retro propulsion.

I can calculate the trajectory due to drag but I don't know how to find it's speed when it reaches the point of maximum heating, at approx 70-80 km altitude.

Does anyone know the best (or easiest!) way to do this? Thank you!

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If you have trajectory, then you have position and velocity over time, so what you need next is aero heating versus velocity. If you can calculate that over the trajectory, you can easily find the peak. If all you care about is the point of maximum heating, you could get pretty close by looking at acceleration times velocity, which should be a good proxy for heat flux. All depends on how accurate you need to be.

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