"Slide into the DMs" is an internet expression for contacting someone through the direct message feature of many possible applications, such as Instagram or Facebook.
While the internet for a long time had a number of good dedicated messenger programs, such as AIM, those were for various and stupid reasons replaced with ancillary message services attached to phone apps or social networking services. to "Slide into the DMs", then, is to go beyond the normal public-facing usage of those platforms to use it for personal communication, with the implied idea that it is an attempt at striking up some type of liaison. Which seems slightly silly to me, since communication is why people use the internet. However, it probably reflects some uncertainty or anxiety with the question of whether the internet is a public or private, social or interpersonal space. Are internet profiles merely for interacting with someone's social persona, or are they a way to form interpersonal relationships? This is the question that the use of this phrase hinges on.