There seem to be three categories for how podcasts deal with ad spots.

Some podcasts mark their ads inline by using Chapter Markers. For example, ATP marks its ads by putting them in a new chapter with a name like "Ad: X". In theory, you could have a player that skips any chapter who's name begins with "Ad: ", though I don't know of any existing apps that do that. Unfortunately, the number of podcasts using chapter markers seems to be a small portion of the podcasts I listen to, so this wouldn't be very useful.

Another method that could work on some podcasts that don't use chapter markers is identifying a delineating tone. Using ATP as an example again, every ad spot starts with the same jingle, and ends with the same jingle. In theory, an app could skip the delineated sections. Mind you, this would require work from the user to set up (or it could be crowdsourced): you would have to tell the app what specific sound snippet delineates the ad read. Luckily, many podcasts seem to be structured in this way, with a clear audio cue to delineate ad spots.

Then, you have really free-form podcasts where the hosts may just say, in everyday speech, something like "time for ads", and the ads will insert. Sometimes it's always the same phrase (e.g., the use of the phrase "the money zone" on MBMBAM), but that's not always the case (e.g., there is seemingly no consistent verbiage in the Aunty Donna Podcast). This category is the most difficult to deal with.

In summary, I don't know of any existing apps that enable skipping ads for any of these three categories. Of the three categories, one is very easy to implement, one less easy, and one quite difficult. All potential solutions would require a shared/crowd-sourced database of which category each podcast falls into, at the least.