Does the Nikon FM-10 35mm SLR Camera have flash?

I can't tell online if it has a flash

Yeah.

It has a hot shoe to take external flash, but there's none built in, Cosina never got around to that (after AF came in, a number of manufacturers engaged Cosina to produce budget MF models for certain markets - the Olympus OM 2000 and Canon T-60 are other examples).

If you want a 35mm SLR, the Nikon FM has a similar specification and better build quality (it WAS built by Nikon), I'd also look at the Pentax MX and Olympus OM-1.

Here is a link to that camera

http://www.nikonusa.com/.../FM10.html" class='ext_link'>http://www.nikonusa.com/.../FM10.html

As you will notice when you read the page this notice:

Flash: Non-TTL method controlled from Speedlight.

A "speedlight" is another word for external flash

The Nikon FM-10 was a made-by-Cosina budget version of the notable Nikon FM, one of my favorite Nikon 35mm SLR's. Neither of these cameras came with a built-in flash, as they depended on external flashes that attached to the hot shoe atop the body.
http://www.nikonusa.com/en/Nikon-Products/Product/Film-Cameras/1689/FM10.html
http://en.wikipedia.org/...Nikon_FM10
http://www.mir.com.my/rb/photography/hardwares/classics/nikonfmseries/fm10/fm10manual/index.htm

Though it accepted almost the full range of Nikon AI and AI modified lenses and was capable of excellent photos, the plastic build of the body (to meet a consumer price-point) was a turn off for me)

I'd suggest looking for either a Nikon FM or N2000 for a full metal bodied 35mm body.