Predicting the likelihood that a prediction from a linear regression model is accurate
In case you are talking about providing certain interval to your predictions, what you might need is adding some confidence interval to your linear regression predictor, something which you can make via a resampling method like bootstrapping as a robust way to find predictions intervals. One key advantage is that it does not assume any kind of distribution, being a distribution-free method to find your predictions and, if needed, to your regression coefficients estimates.
The steps would be:

Draw n random samples (with replacement) from your dataset, where n is the bootstrap sample size
Fit a linear regression on the bootstrap sample from step 1 and predict a value
Take a single residual at random from the original regression fit, add it to the predicted value and save the result.
Repeat 1 to 3 steps several times (1k times for instance)
Find the desired percentiles of your interval (2.5th to 97.5th for instance)
Source of info in this book

On the other hand, if you mean providing a generic confidence metric value for your model, you should find for instance a MSE or MSA on a test set.