Check the individual fonts used in the flyer for their licences. If all are free to use for commercial purposes, you are home free, if not, contact the individual font authors. Naming which fonts are used would get you a more definitive answer.

I think the current system font for iOs devices is San Fransisco. The previous default was, I believe, Helvetica Neue.

'KATLIM 05-15' etc.

'Turkhiphop' (Heavily modified…)

'DUELLO'

Looks very much like Savoye, but the '+' (plus) is wrong… perhaps from another font?
edit: The sample posted is set in Savoye LET, a different cut of Savoye from the link posted, which shipped with Mac Appleworks back in the days of yore:
https://en.wikipedia.org/wiki/List_of_typefaces_included_with_macOS

Depending on style you are after, you could do worse than searching MyFonts for stencil+script and have a look see at the results.
http://www.myfonts.com/fonts/schriftgestaltung/rosa-stencil/
This would probably do the trick for a script…

You could probably do something with Latin as a starting point. There are many cuts but this one offers an Elongated which is not 100 miles away from the sample…

explogos.com
I have CS6 but not CC. As Frd get my email from my profile and I'll have a looksee. If client who's having the issues is on CC however, I probably won't be able to shed much light on the issue as I'm legacy (I prefer to call it retro).

If you mean the one to the right of the illustration with the metallic gradient…

Props to Don for already IDing this one.
http://www.dafont.com/forum/read/302992/font
With some modification (or possibly alternates?)

Hi Nils.
I'm a 'hobbyist' as far as font creation counts, so my software advice is probably best ignored (I use Illustrator to draw the base glyphs and FontForge for everything else). I know I should do the drawing in FontForge, but Illustrator is my 'comfort zone'…
More useful resources to look at
http://briem.net (an extensive 'course' in type design)
http://www.thomasphinney.com/type-design-resources/ (a whole lot of resources)
https://foundry.myfonts.com/guides/#common-errors (a guide to what not to do)
Good luck
Pil

Hi Nils.
Firstly, how long ago did you submit the font? It's not an immediate process between submission and acceptance, so if it was a recent submission, you may just have to be a little patient. If it's not accepted, it's likely to be a technical issue, rather than an aesthetic reason. I think the admins give feedback when a font is rejected, but someone may want to jump in here to confirm that…
My advice on getting feedback. Firstly friends, family and peers and colleagues.
Typedrawers.com perhaps to seek critiques of your work in progress. If you do submit for a critique, just basic upper and lowercase glyphs and numerals. Maybe http://www.typophile.com also for critiques.
Also a rigorous self testing regime. Generate and install the font yourself and test it to destruction in every app it's likely to be used in (Word, Pages, InDesign, Illustrator, PS etc).
I've found this very useful; http://www.impallari.com/testing/ for testing metrics and so forth online at a glance (without the hassle of installing).
You could post here for critiques and queries, but remember, if you have a tech query, be clear about the software you are using (Glyphs, FontLab, Fontforge etc.) so peeps can help if they can.
pil

CHASING (your welcome BTW)