How can I turn rolled oats into flour without a food processor?
You could use a mortar and pestle, if you have a good (and large) one - though it would take a lot of time and grinding to make it work, and probably small batches to fit your mortar and pestle size, it is doable, especially if this is a one-time use.  you would probably not want to do this often, though.

You might try a blender, it's very similar to a food processor if you happen to have one.  I would not recommend an immersion blender, as the oats (and flour) would fly everywhere (as opposed to liquid which holds together a bit more), but a regular blender should work well (also, keep it covered, though).

If you have a coffee grinder, that's also a possibility - it is intended to turn beans into powder, this is just a different grain.  You might want to make sure it's quite clean unless you want coffee flavored cookies, though.

And final option, if you have a spice grinder, that should also work.  Some people get a spare coffeee grinder for the job, or if you have a little hand crank grinder (like some people use for pepper or cinnamon or such), that would also work - though again, lots of work and small batch sizes, but possibly worth it for one time.

Additionally, if you toast the oats a bit, they should be dryer and easier to grind (and toasting gives a bit of flavor) - this will help especially if you're using one of the hand methods, like mortar and pestle or tiny spice grinder.