I second what Alex said in regard to legality but you could also get the fonts if you mimic the Ajax request with requests and bs4:
In [16]: import requests
In [17]: from bs4 import BeautifulSoup
In [18]: data = {
....: 'seed': '24',
....: "text": "Pangrams",
....: "src": "pangram.auto",
....: "size": "72",
....: "fg": "000000",
....: "bg": "ffffff",
....: "goodies": "_2x:0",
....: "w": "720",
....: "i[]": ["fort-foundry/gin/regular,,720", "fort-foundry/gin/oblique,,720", "fort-foundry/gin/rough,,720",
....: "fort-foundry/gin/rough-oblique,,720", "fort-foundry/gin/round,,720","fort-foundry/gin/round-oblique,,720",
....: "fort-foundry/gin/lines,,720", "fort-foundry/gin/lines-oblique,,720"],
....: "showimgs": "true"}
In [19]: js = requests.post("http://www.myfonts.com/ajax-server/testdrive_new-ajax.php", data=data).json()
In [20]:
In [20]: urls = [img["src"] for img in BeautifulSoup("".join(js.values()),"lxml").find_all("img")]
In [21]: pp(urls)
['//samples.myfonts.net/a_91/u/af/5e840d069d35f2c8e5f7077bae7b1e.gif',
'//samples.myfonts.net/e_91/u/d6/1d63ad993299d182ae19eddb2c41e1.gif',
'//samples.myfonts.net/e_92/u/7c/15b8e24e4b077ae3b1c7a614afa8b5.gif',
'//samples.myfonts.net/b_92/u/ce/63dffdda8581fc83f6fe20874714e7.gif',
'//samples.myfonts.net/e_91/u/51/e8b7a0b5cccb2abf530b05e1d3fb04.gif',
'//samples.myfonts.net/b_91/u/6f/a5f870c719dcf9961e753b9f4afd7e.gif',
'//samples.myfonts.net/b_92/u/7c/94d652e4f146801e3c81f694898e07.gif',
'//samples.myfonts.net/b_91/u/47/39fa3ab779cabd1068abbca7ce98c5.gif']
The only ones you need to pass are the i[]: values, the rest can be used to change the size, background colour etc..
So if you did not care about changing the bg, fg or size etc and to get all the names using just bs4 and requests, you could get the font names from the the search-result-item class and construct the Ajax request using those:
In [1]: import requests
In [2]: from bs4 import BeautifulSoup
In [3]: r = requests.get("http://www.myfonts.com/fonts/fort-foundry/gin/")
In [4]: soup = BeautifulSoup(r.content, "lxml")
# creates fort-foundry/gin/regular,,720" etc..
In [5]: fonts = ["{},,720".format(a["href"].strip("/").split("/", 1)[1])
for a in soup.select("div .search-result-item h4 a[href]")]
In [6]: data = {
...: "i[]": fonts
...: }
In [7]: js = requests.post("http://www.myfonts.com/ajax-server/testdrive_new-ajax.php", data=data).json()
In [8]: urls = [img["src"] for img in BeautifulSoup("".join(js.values()),"lxml").select("img[src]")]
In [9]:
In [9]: from pprint import pprint as pp
In [10]: pp(urls)
['//samples.myfonts.net/b_91/u/06/64bdafe9368dd401df4193a7608028.gif',
'//samples.myfonts.net/b_92/u/06/b8ad49c563d310a97147d8220f55ab.gif',
'//samples.myfonts.net/a_91/u/e7/8f84ce98f19e3f91ddc15304d636e7.gif',
'//samples.myfonts.net/e_91/u/71/9769a1ab626429d63d3c779fcaa3d7.gif',
'//samples.myfonts.net/b_92/u/65/fe416f15ea94b1f8603ddc675fd638.gif',
'//samples.myfonts.net/b_91/u/5d/3ced9e71910bc411a0d76316d18df1.gif',
'//samples.myfonts.net/e_92/u/cd/0df987a72bb0a43cba29b38c16b7a5.gif',
'//samples.myfonts.net/e_91/u/88/3f80a1108fd0a075c69b09e9c21a8d.gif']