Do you want to do it well or quickly?
I'm not being facetious, determining divergence times is difficult and if you want to do it for publication you'll have to put some time an effort into doing it right. If, on the other hand, you want to something for your own use or an assignment you might get away with quicker effort.
No matter what you do, you will need to have either an estimate of the rate at which you sequence evolves (in changes per site per million years) or some nodes in your tree you can put a date on (fossils or a biogeographic split). If you want a rough idea of a date from that then MEGA (above) is as good as anything for getting dates.
If you need something a bit more serious then I would look to BEAST. The advantage here is you are including a lot more of the uncertainty in the tree and the molecular clock and the calibration points when you do the dating (of course, that will almost certainly mean wider error bars, but that's often the price of being honest ;).
There is this timetree website that contains authoritative estimate on divergence (in terms of million years) between pairwise species. Otherwise, you'll have to use some molecular markers, e.g. 16S rDNA sequences, and construct the phylogeny yourself.
Already nice answers, here is my thoughts:
Following David's suggestions, I would suggest that you need to put in more thoughts before attempting to quantify the divergence between a given set of species. Getting evolutionary distance in scale of time using tools discussed may provide an abstract way of the diversity pattern based on the data you have. If you are new to phylogeny tree implementation, I strongly recommend a quick read of this article.
In a nutshell: From a bioinformatics perspective, if you are looking at a set of plant species to get a "pattern of divergence" based on a distance matrix. You need to define a dataset (for example sequence (protein, dna or rna) then follow a typical phylogeny analysis pipeline.
Select a reference sequence from each species > BLAST > Alignment > Phylogeny analysis
For phylogeny analysis you may either use tools discussed here or go with the classic tool Phylip. A typical workflow for Protein sequence using Phylip to generate a distance matrix which can be visualised using phylogeny visualization tools will be as follows.
alignment -> seqboot -> protdist -> neighbor -> consense
This will give you an abstract way of divergence among the plant species based on the sequence.
If you just need to get an idea where your species of interest in the tree of life without the sequence based data you may use Timetree as suggested by Haibao.
To Khader's answer, I would add that the dataset to examine can also be the entire genome - specifically the organization of the genome. In similar analyses we have done (with plant genome data), we would ask a question along the lines of how many pieces of contemporary genome X need to be rearranged to compose a contemporary genome Y? Certainly by far the most popular way to measure the "distance" between organisms is in millions of years ago (when they shared a common ancestor). Given that plant genomes have seen tremendous change over time - especially in terms of genome rearrangements and genome duplication/loss - one might very well consider measuring distance between species in terms of large-scale genome changes. For example, one reason wheat is so different is because it is hexaploid. Z. mays saw genome duplication events as well.
In other words, don't lose sight of the bigger picture, often a biological picture, when embarking on the analysis.
Jeff Thorne has stopped focusing on this kind of thing in his work, but has some papers that you might like to look through for help understanding some of the issues involved - he has a link to his publications from his webpage:
Jeff really knows what he's talking about, so he's a good place to go for an authoritative take on this topic