You most likely need to download and import the CSV files from Binance, manually. Go to Wallet > Transaction History > Generate All Statements. Once downloaded, import it on the wallet page on Koinly.
This was not enough to fix my issues though, I also had to import an XLSX file called “Export Deposit History” which I found in Wallet > Transaction History > Fiat > Deposit.
Koinly doesn’t seem to mention importing this second file but it fixed a lot of missing transaction for me. Now my only issue is some 0.1 USDT is missing. Also, for some reason, Koinly reports that my transaction imports show my balances to be double what they actually are. When I look at my wallet on Koinly, the balances are correct (due to API sync) but each currency has an exclamation point next to them, reporting that my calculated balances are double the value that they actually are.
Koinly is kinda working for me but I am hoping something smoother comes along soon, whether that be a Koinly update, a Binance API update or a competitor. I do not want to add every transaction manually, I would sooner pay a crypto tax expert to go through my statements.