Some questions:
1. Were the same chain and freewheel used together during its previous install (I assume you took the parts from another ride).
2. Are you sure it is the freewheel? If you answered "no" to 1., then it could be the chain isn't "matched" to the freewheel cogs (due to a "stretched" chain).
3. Did you push out or install chain pins? If "yes", check for a tight link. If you didn't shorten/lengthen the chain and used a master link (SRAM, KMC, Wipperman), this this is less likely.
4. BTW - I assume the derailleur is adjusted, And the frame is not damaged, such that the frame's rear triangle flexes upon load.