How complex must round constants be to resist slide attacks?
It depends on the actual block cipher and is quite an open problem. For example, SCREAM, iSCREAM and Midori64 use such key schedule (i.e., its absense) with sparse round constants. They were broken with a practical attack on quite large weak key space [1]. Though, the linear layer has some special property.

I would add that its not the slide attack that matters, but symmetries/invariants and these things are not yet well understood.

[1] https://eprint.iacr.org/2016/732