In this paper, the maximum likelihood and the Bayes estimators of the two unknown parameters of the flexible Weibull distribution have been obtained for progressive Interval type-I censoring scheme with binomial random removal. Point estimation and confidence intervals based on maximum likelihood and bootstrap method are also proposed. A Bayesian approach using Markov chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. To illustrate the proposed methods will discuss an example with the real data. Finally, comparing the two techniques through comparisons between the maximum likelihood using bootstrap method and different Bayes estimators using MCMC study.