You still can claim…
You may not have paid any tax in the last three years, but this does NOT mean you are not eligible to claim. It is based on 3 years average net profit. If you were under the personal allowance this would mean you paid no tax – but you still have taxable profit. Of course, to be eligible you have to be affected by the virus and lost income.
It doesn’t say you have to have lost ALL income so I assume they will ask how much your income has reduced by before calculating the grant.
Self-employment income has to be greater than 50% of total income.
As long as you submitted a 2018/19 tax return you should receive a letter from HMRC showing how to claim. I don't know how long they are taking to send these out. I very much doubt it will be an email as they usually contact via letter to ensure it is going to the right person. If you have only submitted one or two tax returns in the last three years because you weren’t self-employed for the entire period, the grant will be based on an average of these. You have to be intending to trade in 2019/20 and intending to send in a tax return – although how they will know this, I have no idea. Maybe it will be one of the questions you need to answer when you apply.
If your income has been affected, you can and should claim Universal Credit (I know the queues are horrendous but hang in there) to see you through the next couple of months as the grant may not be paid until June. The grant may affect your claim for UC as it may take you over the income threshold – therefore in that case I imagine it will have to be paid back.