I was just playing an Sl game and got a escape of 1m 59s speedrun and didn't take a photo but my friend escaped with me and got a 2m 2s escape and got a photo. Is there a way to submit my speedrun with just a photo of escape time? Also I'm gonna wait and see if my scpstats.com will show my escape time and if so I'm gonna show that too!

The simple answer is no, you can't submit a run with just a screenshot. You need a full video of the run from start to finish showing you restart/create the round. Another thing to note is that runs have to be played on a local server by yourself unless you are doing the co-op category. I am not a mod btw so technically it's not a no yet.

Yeah, I'm assuming you were playing online, so it would be invalid anyway even if you had a video. A screenshot is not enough to tell whether or not the time was legitimate. There are probably some other things that would invalidate it too such as the server being modded, escaping as a scientist instead of a class-d, etc.