If you want just 10 boards for prototyping, you might want to check out ITEAD's FPC proto service. You can get 10 small FPC for $100.00.
From a regular manufacturer like Gold Phoenix, for instance, you might have to shell out more than double that to get started. They are gonna charge pretty much the same for 1 board or a whole panel. But you know you can order the production board and it will be exactly the same. And for the higher initial cost, you may be receiving many times as many proto boards. This might be useful if you need more than 10 boards to determine failure rates and manufacturing issues.
If you buy in high enough volume, the price between a vanilla FPC and rigid can be pretty small. FPC is only crazy expensive in small quantities.
do we have some cheap, reliable and online quotation?
Many chinese factories will give anyone quotes. Just take the time to fill out their quote page and upload a gerber. If you're gonna do thru all that trouble, be sure to request quotes for multiple quantities to see what the price:quantity curve looks like. That's what those fields are for. Use them.
BTW, I remember when this was intimidating to me. I talked with some domestic companies. Minimum cost of $1000 for someone to hold your hand through the process. All you really need to know that is different from rigid, as far as buying boards from china, anyway, is a few things. The material is polyimide. It comes in a couple basic thicknesses. 0.1mm or 0.2mm. The soldermask is an additional lamination of polyimide with holes punched in it. You can add additional laminations/stiffeners or adhesive backings for additional charge. Everything else, you can learn from mistakes cheaper than paying someone with experience.