Instagram is a trade name associated with a smartphone App. It takes the extremely high quality images that are now possible with digital cameras and does its best to reduce them to the standard of cameras that were typically available forty years ago.

Since the 'Instagram' effect is in 'post-processing' it can be applied to any photo (if it is good enough to start with!)

The other approach would be to buy a camera that is 40 years old and take pictures with that. The effect that is emulated in Instagram comes from various factors:

1) Film quality
2) Lens optics
3) Camera construction
4) Film processing
5) Aging (fading)

Some of these effects are now difficult to replicate in the real world as the quality of film and processing is better than ever before, aging has less pronounced effect - and takes time! The lens quality on your old camera will be as good or bad as it ever was as will the camera construction quality.

If you take this option, consider each photograph well, you have a limited number of shots per film and you'll not only have to pay for the film but also to process it and print the pictures!