Can a sigma flash be put on a nikon camera?

Can a sigma or canon flash be put on a nikon d3100 camera?

They can but you will lose the automatic features like i-TTL and the ability to use the Nikon Creative Lighting System

You can buy a Nikon refurbished SB-700 for under $300

http://shop.nikonusa.com/....242455800

With the flash and the camera set to manual, you can get the flash to flash if they are different brands. You may need to calculate f-stop from guide number. Exceptions are some like Sony that have a different hotshoe configuration.
If the flash is an older model originally made for film cameras, there may or may not be a problem of high trigger voltage damaging the electronics of a digital camera.
Many older flashes were tested with results shown here:
http://www.botzilla.com/photo/strobeVolts.html

Yes as long as you know what you're doing.