I always use TimeTree, a public resource for knowledge on the timescale and evolutionary history of life.

See on youtube how it works: Kelly explains TimeTree.

In Webb Miller et al's paper, the paper you cite, there is a link to an alignment file, and the data set is also on Galaxy. You can create a newick file (Mammalian examples here) from one of many phylogenetic programs out there: I prefer both RAxML for maximum likelihood based methods (github here) and MrBayes (sourceforge here) for Bayesian analysis. Quick and easy to get a tree with branch lengths from their dataset. I like viewing trees in FigTree.

I searched for a few minutes on Google and didn't find any newick files that were readily available that matched exactly what you want, but that's not to say that they are not out there. You should be able to draw a phylogenetic tree from the dataset they provide in less time than it would take you to search the web for a close approximation and then modify it to match this paper.

If you're really challenged by all of that and can't reproduce their branch lengths for some reason or another and you want to exactly reproduce the phylogenetic tree with branch lengths they show in the supplemental data, then, ultimately, you can use TreeSnatcher to write a newick file from an image.

I already made a matrix with the data extracted from TimeTree. I've found that there are a lot of discrepances with data coming from there and data coming from onezoom.

For instance the divergence time between megabat (Pteropus vampyrus) and microbat (Myotis lucifugus) is 57.5 Million years for timetree.org abd 71.2 Million years in onezoom.org