Krdytkyu

Is there a Ubuntu alternative for this program?

There is a whole Article on Wikipedia dedicated to the Problem.

Unfortunately, it seems there's currently no one solution that works well enough, but a massive list of projects that are underway.

You may want to rummage through the list of solutions to see if there's anything that fits your needs.

Platypus:

There's always the possibility to run Dragon Naturally Speaking using WINE. The Platypus Project is creating software to redirect Dragon's output to any Linux / X application, and they are very far along.

You should definitely take a look at this.

You can install Chromium 11 version from the ppa ppa:chromium-daily/stable (How to add an PPA) and add --enable-speech-input to the end of the launcher.

Now visit this website and whoo! Speech-to-Text on ubuntu using html5.

I read here that if you speak slowly it will be more accurate.

For an updated answer, here is an article from March 2018: Best Free Linux Speech Recognition Tools – Open Source Software.

This article highlights the best open source speech recognition
software for Linux. Note, some of the software is in an early state of
development, and is therefore not ready for widespread adoption.

Before examining our recommendations, Jasper is worthy of a special
mention. It’s an excellent open source platform for developing
always-on, voice-controlled applications. You may be wondering why HTK
doesn’t appear below. For sure, HTK is a popular speech recognition
toolkit. But HTK is not eligible to feature in the recommended
solutions. Not because it’s copyright is owned by Microsoft, but
simply because it’s proprietary software.

Let’s explore the 6 free speech recognition tools at hand. For each
title we have compiled its own portal page with a full description and
an in-depth analysis of its features.

Open Source Speech Recognition Tools

• 
  DeepSpeech TensorFlow implementation of Baidu's DeepSpeech architecture.


• 
  Julius Two-pass large vocabulary continuous speech recognition engine


• 
  Simon Flexible speech recognition software


• 
  CMUSphinx Speech recognition system for mobile and server applications


• 
  deepspeech.pytorch Implementation of DeepSpeech2 using Baidu Warp-CTC.


• 
  Kaldi C++ toolkit designed for speech recognition researchers.

freespeech-vr

Is a decent open source speech to text engine. Here the source code (on Google Code)

Note that it takes a bit of configuration, which is less polished than Dragon Naturally Speaking's configuration.

Dictanote

To expand on Alaukik's answer, there are apps built on top of Chrome speech recognition capabilities.

I personally use Dictanote (it is very similar to Dragon). Here is a link to chrome app.