Did you have any luck finding any supplier for your exact flip-flops on alibaba.com, made-in-china.com etc?
You are right that there are thousands of suppliers, a lot of them selling identical goods, and also you'll be happy to know that most of them don't put all of their products online. Their capabilities are normally greater than shown (not all the time though!).
I work for China 2 West with our HQ based out in China we are the eyes and the ears on the ground, have a look at www.china2west.com.
If you want, send me an e-mail email@example.com with a photo and description of the exact flip-flop you're looking for and I'll get the team to search the local supply source to see what we can come up with.
---Mark ClaytonChina 2 West Services Ltd.303 Ping An Building,Yuan Lin Road, Ji Da,Zhuhai, 519015 China.+86 756 3828382