To gain more reviews on any social platform, I would reach out to your current customer base and ask them to review, you can provide incentive, but you don't have to. Previous clients love to help and it sometimes does lead to repeat business. Always have your pages linked to your email signature as well. It's important that everyone knows you on social media.
I am not familiar with Yelp reviews, but to get reviews on Amazon, you can do several things:
1. Have a great product insert- maybe a coupon code for future purchase, link to sign up to your newsletter etc. On the other side, tell your story about how you are a small business and how you rely on reviews on Amazon and gently urge the buyer to leave a review
2. Use tools like Feedback genius or Salesbacker (I have used it and works great https://www.salesbacker.com/) to send out auto email sequence asking for reviews. You can set them up to send one email right after the purchase, another after they receive it and another after 5-7 days of delivery. You can play with the sequence and see what works for you. Make sure you follow Amazon's policy carefully, otherwise you might get banned.
3. Use groups on Facebook where you can post coupon codes in exchange for reviews, work with the admins of the group to get better results
Hey @Saritha your #2 is spot on as I've posted feedback/reviews after this exact experience. The first one was "want to make sure you received and everything is as expected.." 2nd one was would you be interested in providing feedback, 3rd was the same but also a code for future purchases. I like this process a lot... Less obtrusive that outright stating, "please, please provide a review..."