I don't think using a VPN to log in Binance will trigger any red flag at Binance. The reason is simple: Binance.com was blocked in China a few years ago and all existing Binance users in China had no other choices but to
use a VPN that work well in China (there's even a Chinese word for this:
翻墙VPN) to access Binance. I don't think all those Chinese users will be banned by Binance because they use VPNs.
With that said, I'd recommend ExpressVPN or NordVPN for this purpose, because both of them offer fast speed, good security and many server locations to choose from.