The phrase "and I started speaking" is correct and usable in written English.
You can use it to indicate the beginning of a conversation or a speech after a certain event or moment.
Example: "After the introduction, I took a deep breath, and I started speaking about my experiences."
Alternatives: "and I began to speak" or "and I commenced speaking".
This program came along and I started speaking in class and giving presentations.
I had never really realised how that had affected me, and that's what Oliver and I started speaking about.
"A month later, all this stuff was happening in Sri Lanka" — the Tamil insurgency was being defeated amid reports of thousands of civilian casualties — "and I started speaking up against it.
I went and got ripped, I went and got out of my mind, and I started speaking all kinds of crazy shit 'cos usually back in the days when I used to smoke, it used to broaden my ideas and everything".
After 14 painful years of feeling hopeless and helpless, I started speaking up.
I thought she might take out and dust off an old rehearsal manuscript, but instead she told me to sit down at the table and "Begin!" As I started speaking she sat directly opposite and began waving her hand, conducting me.
And it changes your voice a little bit, but I thought: 'Oh, that's really cool!' And after that I started speaking like that 'ouhhggghhh …'" he replicates the style, and then laughs.
That was only his first time: "When I worked with Fema [after Hurricane Sandy, inspecting housing damaged by the storm], when I went down to Queens, stayed the night and [the residents] looked at me normal until I started speaking and then they knew I was Puerto Rican".
When the list got long enough, I started speaking and writing about it.
That warmth comes from trillions upon trillions of photons cascading through the atmosphere, being absorbed by the atoms in your skin, and causing them to vibrate… When I started speaking, we embarked on a journey together.
I started speaking, doing webinars, and blogging.
