A website that does both or would different websites work? BTC to Monero works really well on
ChangeNow or
SimpleSwap, just don't do anything stupid to trigger the system like visiting it with TOR or sending tainted coins. You can use a residential proxy for something like this.
Do they flag for Tor regardless of small or large amount like say it was $100-$200 usd range?
Yes they do. Most financial services sadly block TOR, but you can't blame them I think they are trying to avoid issues with regulators. Use a good double tunneled VPN with something like tails. Nobody is going to spend a lot of money to investigate this unless you are doing something extremely illegal.
I suppose they ask for KYC too?
Only if the transaction is flagged.