The importance of bioconjugation reactions continues to grow as the need for cell specific targeting and dual therapeutic plus diagnostic medical applications increase. This necessitates new bioconjugation chemistries, synthetic and analytical methods. With this goal, continuous flow bioconjugations were readily achieved with short residence times for strained alkyne substituted carbohydrate and peptide biomolecules in reaction with azide and tetrazine substituted fluorophores. The catalyst and reagent-free inverse electron demand tetrazine cycloadditions proved more favourable than the azide 1,3-dipolar cycloadditions. The use of a fluorogenic tetrazine fluorophore in a glass channelled reactor chip allowed for intra-chip reaction monitoring by recording fluorescence intensities at various positions throughout the chip. As the Diels-Alder reactions proceeded through the chip, the fluorescence intensity increased accordingly in real-time. This novel approach to continuous flow bioconjugation reaction with monitoring may offer advantages over post-chip analysis.