The new couple was snapped walking arm-in-arm in New York's West Village, reported Metro.
The "Too Good At Goodbyes" singer was also seen kissing Flynn as they comfortably walked around, indulging in PDA.
The pictures have surfaced barely a month after Smith, 25, announced that he was "still very, very single".
Flynn, 23, recently came out and declared that he considers himself as a part of the LGBTQ community.
In an emotional Instagram post, the actor had registered his support for the Australian Vote Yes campaign for same sex marriage to be legalised in the country and expressed disappointment when the verdict went the other way.
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