Often times, I think it's hard to handle a chicken in my lap for examination, I prefer sitting or standing them on a table. You may find that you have a bit more control of her when trying to syringe or feed her if you place her on a work surface. To help keep her from flapping around, gently swaddle her in a towel.
If she ever becomes more alert, you may find this helpful - showing how to hold and feed.
If she ever becomes more alert, you may find this helpful - showing how to hold and feed.