Get p-value from fitdistrplus Starting from this question How can I test if my observed PDF follows a binomial distribution?
I have got the following binomial distribution:
require("fitdistrplus")
set.seed(10)
n = 25
size = 27
prob = .4
data = rbinom(n, size = size, prob = prob)
fit = fitdist(data = data, dist="binom", 
                   fix.arg=list(size = size), 
                   start=list(prob = 0.1))

summary(fit)
Fitting of the distribution ' binom ' by maximum likelihood 
Parameters : 
      estimate Std. Error
prob 0.3822225 0.01870338
Fixed parameters:
     value
size    27
Loglikelihood:  -52.24948   AIC:  106.499   BIC:  107.7178 

Is there any way I can get the p-value from the fitdist function?
Or is the p-value prob 0.3822225?
In other words I desire to know if I can state with high level of certainty that my empirical data follow a binomial distribution
 A: The "prob" value there is the estimate of the $p$ parameter of a binomial distribution. It is not a p-value.
To get a p-value, you need to specify a null hypothesis (at least) and typically an alternative (with goodness of fit, the space of alternatives you're interested in may in part define/guide the kind of test you would do, for example if you're doing a likelihood ratio test). 
[However, it is possible to base a test directly off the likelihood under the null.]
There are several issues with performing a test of a distribution you're estimating -- for example not only are you estimating parameters (which may be able to be dealt with - some tests adapt to that more or less easily) but frequently you're also selecting between several choices of distributional model. That impacts the properties of any common test you might want to do. 
There are a wide variety of goodness of fit tests, but they're usually not especially useful (in particular they're often used in situations where they don't really address the problem people want them to solve). [The package fitdistrplus offers a function, gofstat which computes several goodness of fit statistics.]

I desire to know if I can state with high level of certainty that my empirical data follow a binomial distribution

Even if you can get a p-value, it cannot tell you that. You can't determine to a high level of certainty that your sample does come from some distribution since non-binomial distributions can be arbitrarily close to binomial distributions -- there's always room between the data and the distribution you fit to have one that's very like a binomial but a better fit to the data. 
Failure to reject a binomial doesn't mean you have a binomial.
