Practice by reading out loud slowly and enunciating like you want a child to understand you. Do the same with others' speeches, as they were written to be said out loud. If they are recorded in an accent that is in the neighborhood of your goal, even better - you can practice talking exactly like a recording.

Even though this isn't off-the-cuff speaking, you will likely adopt verbal patterns that let your words flow more freely.

You can also join clubs that are dedicated to speaking to other people. If all else fails, something like toastmasters, though that's specifically about public speaking.

If this doesn't go well, that's also okay. You might want to look into a speech therapist if practice doesn't help.