1) Just Do It
No matter how much work you are assigned, you will have downtime. If you've been paying attention around the office, you may have noticed things that should be done, but nobody's had the time to do. Some examples could be:
- Creating an excel spreadsheet to automate a common task (be it something mundane like a business expense report, or the like)
- Creating a computer-readable index of some resource (for instance, create a library of all the company-owned reference books and where they are stored)
- Create a script to improve testing (if you have any sort of repetitive work in your testing, why not use the time to throw together a script to do it)
When you are actively trying to create something to help out everyone, it shows that you aren't averse to hard work, it means you're self-motivated, and if you create something that makes their life easier they will be more likely to ask you to help with other tasks.
2) Talk to your manager
Asking other QA engineers, who aren't responsible for your work, may make them uncomfortable. They are not responsible for keeping you busy, but are responsible for the quality of the work they produce. If you impose yourself on them, they are given the additional responsibility of making sure you do it to their standards.
Going to the manager will give it the official "OK". If your manager says, "That sounds like a great task to teach Korey how to do" then it will be much easier for the other employee to shift the task to you and have it be your responsibility. If you've shown you actually have ability, you are more likely to get better tasks.
3) You are a QA Engineer
If you were keen on being an iOS developer, picking an internship as a QA Engineer probably wasn't the best choice. Rather than being disappointed that a duck is not a pig, how about you start quacking? There is little more miserable than a coworker who seems to think they are above the position they are in.
Perhaps instead of focusing on developing your programming skills, this is a good opportunity to practice your QA Engineering skills instead?