I am designing a mobile app for iOS. What is the base screen size that I can use to start designing the UI of the app so that there won't be any issues while exporting the icons and assets for the developers?
Determining a "base" or "target" screen size depends on several factors. If you have an existing product, a good process would be looking at analytics to understand what type of device is most common for your users. If you're designing and developing a new product, you can make a guess depending on what demographics you think your product will be used by. If you don't know, I'd suggest starting with 375x667 for iOS - that's the size of a iPhone 6,7,8 and is a generally a good place to start.
When it comes to exporting icons and other assets like illustrations, you shouldn't need to worry about making different sizes for different devices. Commonly, your engineers/developers will ask for an asset at 1x, 2x, and 3x, because iOS can intelligently determine which size to serve to a user depending on their device size.
What you might need to provide specs for is how a design will respond at different sizes. For example, if you have 16pt margins on the left and right side of an iPhone 6 design, will those stay the same if you move up to an iPad, or will the margins increase? That's probably the type of stuff you'll need to be thinking of.
As always, your best route will be talking with your engineers/developers and asking them what information they will need. Everyone is different, and you can save yourself a lot of work by simply reaching out and having a quick chat to make sure you're giving them everything they need to execute your design correctly.