Does frequent, uncontrollable flatulence, which prevents one from remaining in a state of ritual purity (tahara), yet sometimes ceases without a specific time, qualify as سلس (sals/incontinence), and in this situation, is it permissible to touch and recite from the Qur’an and perform tayammum for that purpose?

If the emission of wind is continuous, such that it does not cease for a period sufficient for purification and prayer, then you are a person afflicted with سلس (incontinence), and you should perform ablution for each prayer after its time has begun. With this ablution, you may pray as many obligatory and supererogatory prayers as you wish, and you may touch the Mushaf (definition) (copy of the Qur'an) with it. As for reciting the Qur'an without touching the Mushaf, ablution is not a prerequisite for it.

Touching the Mushaf directly (without an interposing barrier) requires ablution, and Tayammum (definition) (dry ablution) is not sufficient unless water is unavailable or one is unable to use it.

A person afflicted with urinary incontinence (سلس البول) has two situations: Either it is continuous and does not stop, in which case he performs ablution when the prayer time begins, takes precautions, and prays, and what is emitted does not harm him. Or, it stops after he urinates, even if after a short period, in which case he waits until it stops, then performs ablution and prays.