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Was it low from a leak?
How much fluid was added?
Did you add the correct fluid?
What is the fluid condition, meaning odor and color?
Most likely the new fluid and the addition of new additives, has cleaned away some of the gunk buildup around the seals and washed it out to be collected by the filter now allowing the previously worn piston seals to no longer be able to hold pressure, which allows the clutches to slip. This would result i na overhaul required.
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Thanks for the update. At this point no the flush is not going to help, likely to make it even worse. The burnt fluid means the clutches have slipped enough to overheat and burn the fluid. Overhaul or replacement is the needed fix.